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JOURNAL OF SEMANTICS Volume 13 Number 3
CONTENTS jOHAN VAN DER AUWERA
Modality: The Three-layered Scalar Square
I
8I
SHALOM LAPPIN
Generalized Quantifiers, Exception Phrases, and Logicality
197
HENRiihTE DE SwART
Meaning and Use of not . . . until
22 I
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Ltarning Morpho·Uxital Probabilitirsfrom an Untagrd Corpus with an Applit'ation to Hrbrrw Moshe l....evingtr. Uzzi Orrun, and Alon lrai
f-------l- J u I I a ---.
Elo:lraolcally brnso lllraugb MIT PnsoJIItltlllb CJialag. Rla:IIJtidlucetpb.llldanllritlglnfotmatltmtiatbl tollowiDg UHL: bHjl�lwww-mltptm.mit.ldu
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Linguistic Highly rnv-,-,..., tur tiS tuownrd �t'llencr rn qu.Uuy ofschobn!Up, ungomtic '"'�"'"' le.ld< tht il�ld In �.uch "" currm• topiCS tn Ungt.mttc throry bsut• ··�· �Ill.·, u l .... ,. you uuuru'O'J of nt>v. theort!ucal J<'\'rlopmcnts b•· presenttn& ehe l.lt�l tn .ntCfl\.lUo"'ll �.trt"h.
Stltct Rtctnt .tnd Iorlhcomills Artide• Thl' <;
,\grf'i·menl ,\twa /lztt•ttr •nil �'' H�lt Nonn·ll�bic An.>l)� ot Vola' As.tnuS.hon m l'c•h�h Jrr:v Rubarh Mort! •>n �Jn.llf$1> lhpotheses ,\Yrl B.tltJII Jrtd I'Jul M PosJAI \'P-lnlt'nW StrUCiun' anJ Objrn 5hin sn
k\'Llndic Chrt1 Colltns a•� llo>sb
m
lttliol,fD lnd -miD-1150 __ .,_to """"....v ,,,,.,.,u'llro o..-U5A ..ws•ro-""' ...... ' �.t.2.e441DQNl�aT �ftt,.. ...,.,m ... -41'11 •tt � •....,, ......, �IIWftf,.,.,.,'t'l Srndeb«• -· U.i ...,, "'UJo 1-....,..,.101-it -"l ��fi"'l: Metll''iiStAn�ID 0rn1•non P.P.�• \.tn raw ,o-.;a'"LS :J, H.y•mt Semi Q!flft1d# M" O:UZ 1)'1'4 � tu •mm�'"''"',..m'"''��......_l.ftt"' forwtiNDtd�artk')r.ab.:tn(tt 01•� W�t);;)rt..-rtw ..nw r. ,,.,...,.,.,....,...,\\rftJ .,_,.... \\•rt� , .__.,) Ub-c. i .u.loo , • \ l ..t.M�.lll.,ai•J -..,,.,,,.,..,.,..,,,_..••
Computatio11al
Computational
Linguistics
Unguistlcs Is the foremost
devoted to
It encompasses AI resntch in language,
journal
linguistics. and rhe psychology of language
exclusively
processing and performance. Wirh each issue
computational
providing applied and theoretical papers, book
analyses
reviews, recltnicaJ correspondence, and leners
•
to the editor, rhc journal presenu a nimularing
of
natural language.
forum for rhe exchange of ideas and nends in computational language. --.
Computational Ungulltlcs is th� journal �rving a
Price� subjecr to chang� wirhout notice.
should be pan of every research library
Pr�paym�nt is required. S�nd check drawn
collection. Recommend Cl to your librarian
against a U. S. bank in U.S. fundi, MC,
today.
VISA. or AMEX number to:
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Computational Linguistia (ACL)
Smith, D. Richard Hipp. Alan W. Biermann
P.O.Box 6090
I
Somerset, NJ 08875 USA
Tel: 908·873·3898
&bust Uarning. Smoothing. and Paramnn Tying on Syntattir Ambipity Rtsolution
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Published quart�rly by
Tung-Hui Chi2ng, Yi-Chung Un, Keh-Yih Su
Tbt MrT Preu for
rhe
Associ:uion for Computational Linguistics ISSN 08912 · 017 . Volume22 forthcoming.
Ltarning Morpho·Uxital Probabilitirsfrom an Untagrd Corpus with an Applit'ation to Hrbrrw Moshe l....evingtr. Uzzi Orrun, and Alon lrai
f-------l- J u I I a ---.
Elo:lraolcally brnso lllraugb MIT PnsoJIItltlllb CJialag. Rla:IIJtidlucetpb.llldanllritlglnfotmatltmtiatbl tollowiDg UHL: bHjl�lwww-mltptm.mit.ldu
____j
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HIrschberg I I I I I I I I I I I
Scope of this Journal The JOURNAL OF SEMANTICS publishes articles, notes, discussions, and book reviews in the area of narural language semantics. It is explicitly interdisciplinary, in that it aims at an integration of philosophical, psychological, and linguistic semantics as well as semantic work done in artificial intelligence and anthropology. Contributions must be of good quality (to be judged by at least two referees) and should relate to questions of comprehension and interpretation of sentences or texts in narural language. The editors welcome not only papers that cross traditional discipline boundaries, but also more specialized contributions, provided they are accessible to and interesting for a wider readership. Empirical relevance and formal correctness are paramount among the criteria of acceptance for publication.
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journal ofSemantics 1 3: 181-19)
© Oxford Universiry Press
1996
Modality: The Three-layered Scalar Square
JOHAN VANDER AUWERA University ofAntwerp
Abstract
1 I NTRODUCTION This paper analyses the semantic and pragmatic relations between the notions of possibility and necessity and of their negations. In so doing it reconciles insights stemming from Aristotle and partially different ones expounded by Hintikka (1 960), Horn (esp. 1 989), and LOhner (esp. 1 990) on the basic quadripartite, tripartite, and scalar nature of the field of modality.
2 SQ UARES The semantic relations between the central modal notions of necessity, possibility and their respective negations have been studied since Aristotle (see Blanche 1 969; Wolf1 979; and Horn 1 989: 6- 21 for discussion and references). It is customary to represent the Aristotelian view with a square, called the 'Aristotelian square' or the 'Square of Opposition'. This square, in the version of Horn (1 989: 1 2) is represented in (1 ) . 'D' stands for 'necessary' and '0' for 'possible'.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
This paper analyses the semantic and pragmatic relations between the notions of possibility and necessity and of their negations. In so doing it reconciles insights stemming from Aristotle and partially different ones expounded by Hintikka, Horn, and LOhner on the basic quadri partite, tripartite, and scalar nature of the field of modality. From Aristotle and his commentators it maintains the Aristotelian square and the view that possibility has two senses, from LOhner the duality square, from Hintikka the tripartite division of the field of modality with one sense of possibility extending over the other sense and over necessity, and from Horn the Gricean scalar analysis of the relation between the two possible senses. This paper further illustrates the basic geometry of modality notions with lexicalization patterns.
182
Modality: The Three-layered Scalar Square
( 1 ) Aristotelian square for modality
'0
p
'
------
subcontrariness
----•
'
0
-.
' p,
'-.
0
p
'
(2) a. 'Op' and '0--. p'f'---. Op' are contrary; they cannot both be true but they can both be false; 'Op' and '0--. p'f' 0 p' are contradictory; they cannot both be true and they cannot both be false; c. 'Op' and '0--. p'f'---. 0 p' are subcontrary: they cannot both be false but they can both be true.
b.
.......
The Aristotelian square also embodies the interdefinability of necessity and possibility: (3) a. Op b. <> p
-
-
...., <> --. p ...., 0 ...., p
In the 1 98os, as of Lohner (1985), most elaborately in Lohner ( 1 990) and in English in Lohner ( I 98 7) a different version has been proposed. It is called the 'duality square'. Lohner's 1 990 version is shown in (4). 'subnegation' is short for 'internal negation', taking one from e.g. 'Op' to '0 ....., p'; 'negation' is the 'external negation', taking one from e.g. 'Op' to '--. 0 p'; duality is the �ombination of external and internal negation, taking one from 'Op' to --. 0 p', which is equivalent with 'Op'. ,
'
.....,
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
On the left, we find positive notions of necessity and possibility. On the right, we find the negative versions: 'it is necessary that not p', which is taken to be equivalent to 'it is not possible that p' at the top, and 'it is possible that not p' and the equivalent 'it is not necessary that p' at the bottom. Some of the terminology which developed throughout the ages is explained in (2) .
Johan van der Auwera
I8
3
(4) Duality square for modality. ' 0 p'
subnegation
•
...,
0 p', '0..., p'
�� �����
'0-.p',
• -.
Op
•
subnegation
'
O p'
3 A T HRE E - LAYERE D D I AGR A M One o f the problems with the squares i n both ( I ) and (4) i s that they can be argued to be incomplete. There is a sense of possibility, illustrated in (s), which does not fit in.
(s) John may be there and he may not be there. This sense suggests the equivalence in (6). (6) Op - 0--. p According to both squares, necessity and possibility are interdefinable as in (3). If this possibility is also the one that the equivalence in (6) deals with, then we end up with the unacceptable result that necessity is the same as impossibility. (7) Dp - --. 0--. p Op - 0--. p .'. D p - --. O p
(- (3a)) (- (6))
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
The elements in both squares are identical, they both embody the interdefin ability of necessity and possibility, but the rest is different. First of all, the positioning is different: on the left top corner we find 'Dp' in the Aristotelian square, yet 'Op' in the duality square. This relates to Lohner's view that the four elements build a hierarchy of markedness and lexicalizability, with the element on the left top corner of the square taking the top position in the hierarchy (Lohner I990: 95-104) . Secondly, the relations between the four elements are different (Lohner I990: 76-8). Thus the two squares do not contradict each other: they just show partially different things. For some semantic fields, only an Aristotelian square has been constructed, for some only a duality square, and for some both. Modality is a field that has been analysed with both squares. But squares are not enough.
1 84 Modality: The Three-layered Scalar Square
Aristotle was aware of the problem, too, and he takes the two senses of possi bility to be different (see Hintikka 1 960; Horn 1 973, 1 989: 1 3-14). He does not, however, appear to have worked out the details of their relation. To that purpose it helps to distinguish the two notions with different names or different symbols. Thus in the reconstruction ofHintikka (196o), the possibility that (6) illustrates is called 'contingency' and the one in the squares retains the term 'possibility'. (8) is a 'diagram' supplied by Hintikka (1960: 20). According to Hintikka, we may also use the term 'possibility' for both meanings, but then we must keep in mind that we are dealing with homonyms. (8) Hintikka's ( 1 960) diagram necessary
impossible
possible
Note that (8) has a basic partitioning in three parts, with Hintikka's 'possible' extending over two of the three parts. (9) is a notational equivalent of this diagram. It does not occur in Hintikka ( 1960), but I introduce it here because its format prepares for what is to come. The contingency subtype of possibility is represented with '+'; the other subtype, the one we know from the squares, retains the '0' symbol.l I n (9), the horizontally arranged parts of (8) appear as vertically arranged layers. Thus the fact that what is possible ('0') is either necessary or contingent ('+') is represented on the horizontal axis in (8), on the vertical one in (9). More generally, in (9) items arranged in the horizontal dimension are compatible with each other. Items arranged in the vertical dimension are incompatible and the totality of these items jointly exhaust the logical possibilities. (9) also shows the equivalences between '+p' and '+ p' and between '-. 0 p' and '0..., p'. -.
(9) Hintikka's ( 1 960) diagram: notational variant 'Op' '+p','+�p'
'0 p'
·�op·,·o�p'
There are two problems with Hintikka's diagram. First, it does not provide for the concept of the not necessary or the possibility not: ' 0 p', '0..., p'. Second, we know with Gricean hindsight-see next section-that the relation between the two uses of 'possible' is not one of homonymy. -.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
contingent
Johan van der Auwera
18 5
4 A S C ALE
(Io) Horn's scale (necessary, possible) (I I) Horn's scale
The assertion of the lower, less informative statement '0 p' instead of the higher, more informative statement 'Dp', conversationally implicates the negation of the higher statement i.e. '--. D p'. When 'p' is possible yet not necessary, '--.p' is possible too. The sense of possibility allowing both 'p' and '--.p' to be possible is 'Op'. Hence 'Op', resulting from the literal meaning 'Op' and the implicature '--. D p' is also an implicature.3 To say this in symbols, with .... for 'implicature': •
(12)
a.
Op ...... -.op
b.
op
Op
...... -.op =
:. 0 p
0p ......
1\
0p
( (l2a)) =
-.
0p
(from (9))
•
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
When Horn (r989: 13) discusses Aristotle's problem with two notions of possibility and represents Hintikka's diagram, he calls it a 'scale'. To call something a 'scale' rather than a 'diagram', the elements making up the scale must not merely be ordered, there must also be a dimension along which the elements have increasing values. I don't see any reason for attributing a scalar idea to either Hintikka (I96o) or Aristotle, but it is clear that when Horn (I 989) presents his own analysis of the modal field and of Aristotle's puzzle in particular, the notion of scale is central. In Horn's view, 'Op' is a scalar Quantity implicature of 'Op'. He first expressed this idea in Horn (1972: I 17), and restated it on many occasions. The essential idea is widely accepted (e.g. Parret I 976; Gazdar 1979: s6; Levinson I98 3: I64) and I too accept it. The scale Horn uses is shown in (ro).2 The higher value 'necessary' is left of the lower value 'possible'. ( II) is my notational variant. I represent the direction of the scale with the dashed arrow, going from lower to higher.
1 X6 Modaliry: The Three-layered Scalar Square
Note that though Horn accounts for the relation between 'Op' and ··p·.
)
scale ( 10)/( I I itself has no place for •• p'. The scale also has no place for the
impossible,'..., <) p' or 'D..., p', either, nor for the not necessary,'..., D p' or'<) ...,
p'. One could retort that the scale was never meant to have these provisions, its main purpose being to offer a Gricean account of the relation between'<) p' and 'Op'. So be it. Horn's scale, therefore, is at best only a part of some more encompassing representation-square, diagram, or scale-of the entire modal field:� Horn's scale docs, however, have a secondary purpose, namely to explain the weak lexicalizability of'...,
D p'. The explanation goes as follows:'..., D p' is
the scalar Quantity implicature of 'Op' and, given the generality of this implicature, there should '
...,
ceteris paribus be no need for separate lexicalization of
arc not really that clear, as Horn English
not possible
( I gXg:
260) is well aware. It is correct that
impossible, and that not necessary docs not in necessary, and Horn plausibly argues that unneces
is lexicalized in
have a lexical counterpart
sary, which docs exist, docs not actually fill this gap. On the other hand, in the case of English modal auxiliaries, may not only marginally contracts to mayn't, while the contraction of need not to needn't is fully normal. Second, even if the facts do lend support for an overall weakness in the lexicalizability of'--.0', the explanation is doubtful (sec also Lohner I 990: 96-7). When something is not necessary, it may indeed be just possible and if this were an equivalence, then indeed there would be no need for a lexical item directly expressing the meaning of 'not necessary', given that there is already a lexical item used for just possible'. However, it is not an equivalence: when something is not
)
necessary, it may also be impossible. Of course, on the scale in ( 10)/( I I , negating what is necessary docs amount to what is only possible, but this is only because this scale is not complete. The desired non-equivalence between non-necessity and possibility is easy to represent if one goes back to Hintikka's diagram. In (9) the diagram docs not yet contain the non-necessary, but it can easily be added, as a mirror image to '<)'possibility. just like 'Op' is either ·�p' or
'
Dp
',
so'...,
D p' is either ·�p' or
'D--.. p'. ( I 3)
Enriched Hint ikka diagram
Op,-. 0-.p -.Op,O-.p
OP. 0 -.p
Op,-.0-.p
o-.p,-.Op
( 3) is not scalar, but we will soon see how it can be given a richer
Of course, I
interpretation.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
D p'. I sec two problems with this though. First, the actual lcxicalization facts
Johan van der Auwera 187
One more remark on lexicalizabiliry. I have so far only discussed this in relation with the implicature in ( 1 2a). But one can also apply the argument to the implicature in (1 2b), aiming to show that there is no or little need to lexicalize '0 ' and '+' possibility separately. In this case, the account fares much better. I do not know of any-language that has the required double lexicalization for 'possibility'. To use an Occam-type phrasing suggested by Larry Horn (p.c.), perhaps no language multiplies senses beyond j ust one 'possible'. More generally, I do not know of any language having separate lexical items for scalar concepts differing only in that one is a scalar Quantity implicature of the other.
Part of the problem with Horn's scale in ( r o)!(r r ) is that it is incomplete. Horn does, however also present an expanded picture in that he argues ( 1 989: 236, 325) that the scale in (ro)/(I I), which is deemed positive, as well as the corresponding negative one in (I4)/(r 5) can be overlaid on the Aristotelian square in {I), thus resulting in what could be called the 'scalar square' in (r6). (I 4) Horn's negative scale (necessary not, possible not) (I 5) Horn's negative scale
(I 6) Horn's scalar square - Aristotelian square with overlay of Horn's scales ' 0 p'
contrariness
' 'D.., p ,
'
.., 0 p
'
� �dWrori� � ���
' 0 p'
subcontrariness
'
0 .., p',
'
.., 0 p'
Is ( I6) the desired complete map? No, it is not, for there is still no place for '+p'. Can ( I6) yield the basis for a correct explanation of the weak lexicalizability of ' 0 p', assuming this to be a fact? No, at least not in an obvious way. ' 0 p' does enter the picture, but it does so on the right-hand scale. Its weak lexicaliz--.
--.
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5 A S CALAR S Q UARE
Johan van der Auwera 19 1
'You mustn't die.' ('0 -. p') lit. 'It is not necessary that you die.' ('-. 0 p') In the fourteenth century, he claims, the two interpretations appear to have existed. Nowadays only the '0 -. p' reading survives. I would interpret the earlier coexistence of the two readings as an instance of an identical lexicalization of two adjacent meanings. This would be similar to what we find in (24). In both cases, we have a unique lexicalization for a vague meaning and for one of the two more specific interpretations of the vague meaning. In (24) the specific meaning was '0 p', now it is '0--. p'. (26) Scalar three-layered square
(27) Scalar three-layered square
Op.O-.p 0-.p,-. 0 p
This is the case for Old English motan or for present-day Danish mtitte, both translatable with 'may' as well as 'must' (see e.g. Ramat 1972; Gamon I993: I S46I; Allan, Holmes, & Lundskxr-Nielsen I995: 294-5). Both have 'Op' as the original meaning, and 'Op' arguably as an Informativeness/Relation impli cature, with in the case of English, bur not Danish-yet also German and Dutch-the implicature ousting the original meaning.
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This makes sense, as argued by Horn (I989: 26I-2), in a scenario of '--. 0 p' originally having the '0-. p' reading as what has been called an 'Informative ness' (Atlas & Levinson I98 I ) or 'Relation' (Horn I984) implicature, a process whereby a statement directly implicates a more informative one, and not, as with a Quantity implicature, the negation of a more informative statement (see also Levinson I983: I46-7). This implicature would then conventionalize and oust the original literal meaning. A similar phenomenon is arguably found with 'Op'. That 'Op' and 'Op' have an identical lexicalization is entirely uncontroversial. This was symbolized in (22). But we also find a situation of an identical lexicalization for '0 p' and for the second adjacent reading of 'Op', viz. 'Op'.
192 Modality: The Three-layered Scalar Square
4. 4.
: : : : '
' ' ' ' ' ' ' '
'
'
....... '
' '
: v
The account has a balance of+ 200 $. The account has a balance of+ 100 $. The account has a balance 0 $. The account has a balance of- 100 $. The account has a balance of- 200 $.
On the Janus scale in (28) entailment cannot involve the middle value, nor can it cross it. Thus though a credit of +2oo$ entails a credit of +wo$, it entails neither a balanc� of o$ nor one of- 100$. On the opposite side of the midpoint, entailment holds in the opposite direction. Thus having a debit of 2oo$ entails having a debit of 100$. The positive entailment based subscale from +1 to +co$ and the corresponding negative one support implicatures in the ordinary way, but the scale as a whole also does. In a context of specifying how rich one is, the assertion that one has - wo$ may implicate that one does not have o, + 1 oo or +2oo$-the negation of the higher values-and the direction of the scale in (28) is then from negative to positive. Conversely, in a context of specifying how poor one is, the assertion that one has +wo$ may implicate that one does not have o, -wo or -2oo$-the negation of the higher poverty values-and in this case the direction of the scale in (28) is from positive to negative. The th�ee-layered square of modality scale is another illustration of a Janus scale. The midpoint is 'pure' possibility 'Op'/'� ....., p'. From there one can look up or down. In both directions one looks at the necessity of something, but in the upward direction, it is the necessity of a positive 'p' ('Dp'), while in the negative direction, it is the necessity of a negative 'p' ('0 p'). Equivalently, one can also say that one looks at the impossibility of the negation ofsomething, but in the upward sense, it is the impossibility of the negation of a positive 'p' ('--.. .....,
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The point of this paper is not to study lexicalization as such, however.5 It is rather to decide on the 'geometry' of modality notions, and on this topic I am claiming that it makes sense to think of modality in terms of the scalar three layered square shown in this section. About scalarity there is one more point to be made. In (21 ) and (23) we see that the three-layered square includes two scales. On both occasions, the scales involve two of the three layers. There is, however, a sense in which the entire square is scalar. In other words, there is a scale encompassing all three layers. However, it is not a unidirectional scale like the ones discussed so far, but a bidirectional one, which I hinted at in van der Auwera (198 5: 1 40-1) with the term Janus scale' (see also Lehrer & Lehrer 1 982 and Westney 1 986). A Janus scale has a midpoint, at which, like the god Janus, one can look in two directions, with what one sees in one direction being the mirror image of what one sees in the other direction. An example is a financial debit-credit scale as in (28). Its midpoint is 'o$', the place where the debit balances with the credit.
Johan van der Auwera 1 9 3
7
CONCLUSION
I n this paper I have analysed some o f the semantic and pragmatic relations between the notions of possibility and necessity and their negations. I have done this with the three-layered scalar square in (1 3). (1 3) contains a square. As such (1 3) is in conformity with the Aristotelian square as well as with Lohner's duality squae, but it does more. ( I 3) has three layers. As such it is in conformity with Hintikka's (1 960) reconstruction of Aristotle's views on modality, but it shows more. (13) is also scalar. As such it copes with some ofHorn's insights on the scalar nature of modal concepts and of scale-induced implicarures, but it does more. The paper further contains some comments on the lexicalizability of these modal notions, but it also calls for more research, which, I believe, forces one to distinguish between subtypes of modality like deontic and epistemic modality. Another issue which is left for further research is whether and how the three layered scalar square hypothesis applies to quantifiers and conjunctions and any other notions that have been treated with either an Aristotelian or a duality square or with both. Acknowledgements
Thanks are due to Carla Bazzanella, Larry Horn, and Davide Ricca for their comments, and to the Belgian National Science Foundation and the Research Council of the University of Antwerp for their financial support. JOHAN VAN DER AUWERA
Universiteit Amwerpen (UIA) Linguistiek (GER) B-z61o Antwerp Belgium e-mail: [email protected]
Received: Revised version received:
09.02.96 1 ).04.96
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0 ...., p'), and in the negative sense, it is the impossibility of a positive 'p' ('---. 0 p'). Evidence for thinking that the modal square is scalar across its three layers comes from the interpretation of '-. 0 p'/'0 ......, p'. Up to now, I have charac terized it as 'p' is 'not necessary', which is the same as '-..p is at least possible if not necessary'. But it can also be characterized as 'p is at most possible'. This means that 'p' is definitely not necessary and it allows that 'p' is actually impossible. This characterization amounts to covering the middle and bottom layer in terms of a scalar direction involving the top layer. Similar evidence comes from the interpretation of'Op'/ '-.. 0...., p', interpretable not only as 'p is at least possible if not necessary' and as '---.p is not necessary', but also as '---.p is at most possible'.
I 94 Modality: The Three-layered Scalar Square
N O TE S not wanting to include ··p· in any scalar representation: (i) ·•' is a non-scalar notion, and (ii) ·�· (?probably) does not lexicalize separately. I agree about both points, but I would not say chat these points militate against a possible inclusion of •• p' on a scale. On the first point, I agree that ··p· is non-scalar, but as I will argue in section 6, there is a type of scale that has a non-scalar middle point, and chis is precisely the type of scale that we need for modality. On the second point, even if ·�' does not lexicalize separately, it is a meaning or, if one prefers, an interpre tation, and the scalar representation that I want and which was foreshadowed by Hintikka ( I 960) is a representation of meaning as such, not of lexicalized mean ing. As mentioned above, lexicalizability is a concern for both Lohner and Horn. The most recent and the most cross-linguistic contribution to chis topic is De Haan ( I 994).
RE FE RE N CE S Allan, Robin, Holmes, Philip, & Lundskxr Nielsen, Tom ( I995), Danish: A Compre hensive Grammar, Routledge, London. Atlas, Jay David & Levinson, Stephen C. ( I98 I), 'It-clefts, informativeness and logical form', in Peter Cole (ed.), Radical Pragmatics, Academic Press, New York, I 6 1. Blanche, Robert ( I 969), Structures Intellect
uelles: essai sur /'organisation systematique des concepts, Vrin, Paris. Burton-Roberts, Noel (1984), 'Modality and implicature', Linguistics and Philosophy, 7, I8I-296. De Haan, Ferdinand ( I994), The interaction of negation and modality: a typological
study', doctoral dissertation, University of Southern California. Gamon, David ( I993), 'On the development of epistemicity in the German modal verbs mogen and mii.sse n', Acta Linguistica His torica , XIV, 125-76. Gazdar, Gerald ( I979), Pragmatics: Implicature, Presupposition and Logical Form, Academic Press, New York. Hintikka, J. Jaakko J. ( I 960), 'Aristotle's dif ferent possibilities', Inquiry, 3, I 8-28. Horn, Laurence R. ( I972), 'On the semantic properties of logical operators in English', unpublished doctoral dissertation, Uni versity of California at Los Angeles. Horn, Laurence R. ( I973), 'Greek Grice', in
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This notation, using filled and hollow diamonds, is typographically more con venient than Horn's, who fills the dia monds with either a '2' for contingency possibility, also called 'two-sided possibil ity', or a ' I' for the other type of possibility, called 'one-sided possibility'. 2 For the epistemic reading of modality, 'probable' has been proposed as a value intermediate between 'epistemically necessary' or 'certain' and 'epistemically impossible' (see Horn I 989: 232). I will not go into this. Another issue to be glossed over here is that of the inclusion of the non-modal value 'p', similarly intermedi ate between 'necessarily p' and 'possibly p' (see Burton-Roberts I 984 and Horn I990: 464). Here and elsewhere the phrasing of a state ment or proposition implicating some thing is short for saying that a speaker, who uses this statement or proposition in a given context, implicates something. 4 Larry Horn (p.c.) mentions two reasons for
Johan van der Auwera 1 95 Claudia Corum, T. Cedric Smith-Start, & Ann Weiser (eds), Papers from the Ninth
Regional Meeting Chicago Linguistic Meeting, Chicago Linguistic Society, Chicago, 20514. Horn, Laurence R. ( 1984}, 'Toward a new taxonomy for pragmatic inference: Q-based and R-based implicarure', in Deborah Schiffrin (ed.), Meaning, Form and
Use in Context: Linguistic Applications,
Sixteenth Annual Meeting of the Berkeley Linguistics Society, Berkeley Linguistics Society, Berkeley, 454-7 I. Lehrer, Adrienne & Lehrer, Keith (I982), 'Antonymy', Linguistics and Philosophy, 5, 48 3-50 1 . Levinson, Stephen ( I9 8 3), Pragmatics, Cambridge University Press, Cambridge. LObner, Sebastian (I985), 'Natiirlichsprach liche Quantoren: Zur Verallgemeinerung des Begriffs der Quamifikation', Studium Linguistik, 17/18, 79- I I3.
Discourse Representation Theory and the Theory of Generalized Quantifiers, F aris, Dordrecht, 5 3-85. LObner, Sebastian ( 1990), Wahr neben Falsch:
Duale Operatoren als die Quantoren natiir licher Sprache, Max Niemeyer Verlag, Tiibingen. Parret, Herman ( I976), 'La pragmatique des modalites', Langages, 43,47-63. Ramat, Paolo (1<)72), 'Die Analyse cines morphosemantischen Feldes: die germa nischen Modalverben', IndoY,ermanische Forschungen, 76, 1 N-202. Schmidt, Helmut (1966), 'Srudien iiber modale Ausdriicke der Norwendigkeit und ihrer Yerneinungen: Ein Oberset zungsvergleich in vier europaischen I n aug u ral-D isse rtatio n , Sprachen', Tiib inge n. van der Auwera,Johan (19Xs). Lallf.Uage a11d Logic, Benjamins, Amsterdam. Westney, Paul ( 19X6), 'Notes on scales ', Lilzgua, 69, 3 3 3-S+· Wolf, Ursula ( 1979), M·�t:lichkeit und Not wendigkeit bci Aristoteles wzd lzeute, Fink, Munich.
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Georgetown University Press, Washing ton DC, I I -42. Horn, Laurence R. ( I989), A Natural History of Negation , University of Chicago Press, Chicago and London. Horn, Laurence R. (1990), 'Hamburgers and truth: why Gricean explanation is Gricean', in Kira Hall, Jean-Pierre Koenig, Michael Meacham, Sondra Reinman, & Laurel A. Sutton (eds), Proceedings of the
LObner, Sebastian ( I987), 'Quantification as a m�or module of narural language seman tics', in Jeroen Groenendijk, Dick de Jongen, & Martin Stokhoff (eds}, Studies in
journal ofSemantics
13: 197-220
© Oxford University Press 1996
Generalized Quantifiers, Exception Phrases, and Logicality
SHALOM LAPPIN School of Oriental and African Studies University ofLondon
Abstract
I INTRODUCTION I t is possible to distinguish two main approaches to the syntax and semantics of noun phrases. On the Fregean view, the class of NPs is partitioned into two distinct categories. Proper names correspond to constants which are arguments of predicates. Quantified NPs are treated as expressions in which the determiner denotes a unary quantifier and its N ' is a predicate restricting the domain of the quantifier. Therefore, the logical syntax of ( I a) is (I b), while that of(2a) is (2b). (I) a. b. (2) a. b.
John sings. SingsU) Every student sings. ltx(Student(x) :J Sings(x))
Higginbotham & May ( I 98 I ), Higginbotham (I98 s), and May (I985, I 989, and I 99I) have developed the Fregean view within the framework of
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On the Fregean view of NPs, quantified NPs are represented as operator-variable structures, while proper names are constants appearing in argument position. The Generalized Quantifier {GQ) approach characterizes quantified NPs as elements of a unified syntactic category and semantic type. According to the Logicality Thesis {May 199 1), the distinction between quantified NPs, which undergo an operation of quantifier raising to yield operator-variable structures at Logical Form (LF), and non-quantified NPs, which appear in situ at LF, corresponds to a difference in logical status. The former are logical expressions, while the latter are not. Using van Benthem's ( 1986, 1989) criterion for logicality, I extend the concept of logicality to GQs. I argue that NPs modified by exception phrases constitute a class of quantified NPs which are heterogeneous with respect to logicality. However, all exception phrase NPs exhibit the syntactic and semantic properties which motivate May to treat quantified NPs as operators at LF. I present a semantic analysis of exception phrases as modifiers of GQs, and I indicate how this account captures the major semantic properties of exception phrase NPs. I explore the consequences of the logically heterogeneous character of exception phrase NPs for proof-theoretic accounts of quantifiers in natural language. The proposed analysis of exception phrase NPs provides support for the GQ approach to the syntax and semantics ofNPs.
1 98 Generalized Quantifiers, Exception Phrases, and Logicality Chomsky's Principles and Parameters model of grammar. 1 They propose a rule of quantifier raising (QR) which adjoins quantified NPs to VP or IP. This rule creates an abstract (non-overt) level of syntactic structure, logical form (LF), in which a quantified NP is an operator binding a syntactic variable (an A' -bound trace) in its original argument position. These structures provide the input to rules of semantic interpretation which take quantified NPs to be restricted quantifiers and the traces which they bind to be bound variables. Names are not within the domain of QR, and so they remain in situ at LF, where they are interpreted as referring expressions. (Ja, b) are the LFs of ( Ja, b) respectively. (3) a. [IP [NP John) [VP sings]] b. [IP· [NP every studenth[IP t1 sings]] (4) a. Most students completed a paper. b. [IP· [NP most students]1 [t1 [VP· [NP a paperb[VP completed t2]]] c. [NP· [NP a paperb[NP most students]J] [IP t1 completed t2] (4b) corresponds to the reading of (4a) on which most students receives wide scope, by virtue of the fact that most students asymmetrically c-commands a paper in this structure. In (4c) most students and a paper c-command each other, and so either NP can be interpreted as having scope over the other. Therefore, (4c) does not uniquely determine the scope interpretation of the quantified NPs in (4a) and can feed a wide scope reading of either NP.2 May (199 1 ) suggests that the property of logicality is the criterion for distinguishing between quantified and non-quantified NPs. Those NPs which correspond to restricted (unary) quantifiers are constructed by the application of a logical determiner (determiners which denote logical quantifiers) to an N'. In a sense which will be made precise in section 2 , such NPs can themselves be regarded as logical terms (more precisely, as corresponding to logical functions). Non-quantified NPs, on the other hand, are non-logical expressions. May ( 1 991) makes logicality a necessary condition for the application of QR to an NP. He states that one of the central properties of LF is that it represents the syntactic structure of logical terms, particularly quantified expressions. The assertion that the distinction between logical and non-logical NPs correspnds to a difference in syntactic category and semantic type is an interesting empirical claim concerning the organization of categories and types in the grammar of natural language. I will refer to this assertion as the Logicality
Thesis.3
Generalized quantifier (GQ) theory provides an alternative to the Fregean analysis of noun phrases.4 On the GQ view, NPs constitute a unified syntactic category and semantic type. Names and quantified NPs are not factored into .distinct types. Every NP denotes a set of sets (or a set of properties), while a
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(4b) and (4c) are the two possible LF representations of (4a).
Shalom Lappin
1 99
determiner denotes a function from a set to a set of sets (alternatively, a determiner denotes a relation between sets). (sa-c) illustrate the way in which names and quantified NPs receive interpretations of the same type within the framework of GQ.
(s ) a. IUohn ll - (X s;;; E: j E X) b. II every student II - (X s;;; E: Students s;;; X) c. II most students II - (X s;;; E: I Students n X I > I Students - X I ) (6a-c) indicate the truth conditions for (1a, za) and Most students sing, respectively, given the interpretation of their subject NPs specified in S ·
In contrast to the Fregean view, the GQ account takes logicality to be orthogonal to the category of NPs and the semantic type with which it is associated. In this paper I consider the interpretation of exception phrase NPs, like the subject of (7a) and (7b), in the context of the debate between the Fregean and the GQ approaches to the representation of NPs. (7) a. Every student except John arrived. b. No student except John arrived. I argue that these NPs provide an important set of counter-examples to the Logicality Thesis that NPs are sorted according to logicality at the level of syntactic structure which provides the interface to semantic interpretation. Specifically, exception phrase NPs are heterogeneous with respect to logicality, but all members of this subcategory exhibit semantic and syntactic properties typical of other quantified NPs. This distribution of features within a subclass of quantified NPs is incompatible with the Logicality Thesis version of the Fregean approach, but it is entirely natural on the GQ account. In section 2 I review the concept oflogicality which provides the basis for the categorial and type distinctions which Higginbotham and May seek to make between quantified and non-quantified NPs. I specify the generalized sense of logicality in which an NP (rather the determiner of an NP) can be a logical term. In section 3 I take up the interpretation of exception phrases. I consider four recent proposals for handling exception phrases, and I suggest an alternative account which, I argue, captures the major semantic properties of these expres stons. In secton 4 I discuss the implications of the proposed analysis of exception phrases for the relation between logicality and the representation of NPs. I also
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(6) a. IUohn sings I - t iff Sings E (X s;;; E: j E X) iffj E Sings b. II every student sings II - t iff Students s;;; Sings c. II most students sing II - t iff I Students n Sings I > I Students - Sings I
200 Generalized Quantifiers, Exception Phrases, and Logicality
consider the consequences of this analysis for recent attempts to develop deductive models of natural language quantifiers. 2
L O G I CAL I T Y
(8)
(9) a. every: a = o b. no: c = o c. some: c � I d. at least five: c � s e. most c > a
A
8
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Mostowski (1957) characterizes a unary quantifier as a logical constant iff its interpretation remains constant under all permutations of the element of the domain E, where a permutation is an automorphism of E which respects the cardinality of the subsets ofE. Lindstrom (1 966), van Benthem (1 986, 1 989), and Sher ( 1 99 1 , 1 996) progressively generalize this notion of logicality across syn tactic categories to define a logical constant as a term whose interpretation is invariant under isomorphic structures defined on E. If we apply this characterization of logicality to determiners, we can specify the set of logical determiners as the set which includes all and only those determiners denoting relations that depend solely upon the cardinality of the sets among which they hold and the cardinality of the intersections of these sets. Following Westerstihl (1 989) I will also assume that, in addition to the condition of permutation invariance for isomorphic structures defined on E, logical determiners satisfy Conservativity and Extension. A binary determiner det is Conservative iff, for every A, B � E, B E det(A) � (A n B) E det(A). A binary determiner det satisfies Extension iff, for any two models M and M ', and any A � E, if A � M � M ', then detm (A) - detm {A).5 It is possible, then, to give the interpretation of a logical determiner as the cardinality values which apply to these sets if the relation denoted by the determiner holds. For the sets in (8) let a = l A - B l , and c = l A n B I . Examples of cardinality definitions for logical two place determiners are given in (9).
Shalom Lappin
201
Following van Benthem (r 986, 1 989), we can characterize the set of logical NPs as in r o. r o. NP is a logical GQ iff, for every permutation n[P] E II NP II ·
7l
of E, P E II NPII iff
(r r) a.
Books
b.
Books
About CS
About Unguistics
( 1 2) a. c - c b. Every/no/some/at least five/most books are about computer science. �
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(ro) is an extension to restricted quantifiers of van Benthem's general characterization oflogicality for polyadic quantifiers. In (ro) a permutation n of P respects P's cardinality and the cardinality of all other subsets of E in the models M for which II NPII is defined. Specifically, if NP is a restricted quantifier, n of P respects the cardinality of the intersection of P with the N' restriction set of II NP II · This requirement on permutations ofP has the effect of causing the truth-value of sentences in which the subject NP is a logical GQ to depend solely upon the cardinality of the restriction set of the subject NP, and the cardinality of the intersection ofP and this restriction set. Clearly, proper names do not satisfy (ro). John may be a singer but not a dancer, even if the set of singers and the set ofdancers have the same cardinality. For the case of a restricted NP obtained by applying a determiner to an N', the contrast berween logical and non-logical NPs is illustrated in (r r ) and (12).
202 Generalized Quantifiers, Exception Phrases, and Logicality
c. Every/no/some/at least five/most books are about linguistics d. Mary's books are about computer science. <1> e. Mary's books are about linguistics
3 T H E I N TE R P RE TA T I O N O F E X CE P T I O N P H RASE N P S 3.1
Previous analyses ofexcep tion phrases
It seems reasonable to require that any adequate account of exception phrase NPs should provide a compositional representation of the way in which the exception phrase (and its argument NP) contribute to the NP in which it appears. Moreover, there are at least three characteristic semantic properties of exception phrases which such an account could capture.6 First, the argument of the exception phrase falls under the N ' restriction of the NP in which the exception phrase appears. Therefore, both (7a) and (7b) imply that John is a student. (7) a. Every student except John arrived. b. No student except John arrived. Second, (7a) implies that John did not arrive while (7b) implies that he did. Finally, as { 1 3) illustrates, exception phrases can only be applied to NPs with universal determiners.
( I 3) a. *Five students except John arrived.
b. *Most MPs except the Tories supported the bill. c. *Mary spoke to many people except John. d. *Not many students except five law students participated.
In this section I will briefly consider four recently proposed analyses of exception phrases in light of these conditions of adequacy. K&S treat exception phrases as components of complex one-place
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When we keep the N' set Books constant and take the cardinalities of the relevant sets in (1 1a) and (1 1b) to be as indicated in (1 2a), the equivalences between (1 2b) and (1 2c) hold by virtue of the fact that the NPs in the subject position of these sentences satisfy the condition in ( I o). However, assuming that all of Mary's books are about computer science but none of them are about linguistics, (1 2d) and (1 2e) are not equivalent. Therefore, Mary's books is not a logical NP. The Logicality Thesis can be formulated as the claim that, at the level of syntactic representation which constitutes the interface to semantic inter pretation, logical NPs are expressed as operator-variable chains while non logical NPs appear in argument position.
Shalom Lappin 203
determiners. They suggest that every . . . except John and no . . . except John are instances of such complex determiners, which receive the interpretations in (r 4a) and (1 4b), respectively. (14) a. B E II every A except John II iff A n B' - Uohn) b. B E II no A exceptjohn ll iff A n B Uohn) =
( r s) a. Each/any/all student(s) except John can take the course. b. None of the students except John took the course. Similarly the K&S account does not exhibit the general contribution of the NP argument of except to the meaning of the containing NP. As the cases in (r6) show, a wide range of NPs can occur in the argument position of an exception phrase.
(r6) Every student except five law students!John and three physics students/ five computer science students and at most rwo logic students participated. Hoeksema (1991) treats exception phrases in NPs (which he refers to as
connected exception phrases) as NP modifiers. He proposes (17) as the inter pretation of exception phrase NPs. (17) II NP 1 except NP211 - (X � E: 3Y: X - Y E II NP 1 11 E-Y & Y E II NP211 }
He supplements ( 1 7) with ( r 8), which, on his view, can be regarded either as part of the semantic interpretation ofexception NPs, or as a Gricean implicature. The conjunction of ( 1 7) and ( 1 8) provides a compositional representation of the contribution of exception phrases to the NPs which they modifY. Moreover, it appears to entail the first rwo characteristic semantic properties of exception phrase NPs. To see this, consider (7a), for example. Hoeksema's analysis implies that this sentence is true iff there is a set Y containingJohn such that (Students) - Y � [a: arrived) and [Students) � [a: arrivedj. It follows that Uohn) � (Students) and that Uohn) g; [a: arrived). To restrict the application of exception phrases to quantified NPs with universal determiners, Hoeksema defines the domain of exception phrase modifiers as the set ofNPs which satisfY the conditions in (1 9a, b).
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This analysis of exception phrases is inadequate in that it does not provide a unified compositional representation of the role which these phrases play in the interpretation of the NPs in which they occur. Specifically, it does not indicate how (14a) and (r4b) follow from a general rule for computing the meaning of an NP in terms of the meanings of its N', determiner, and exception phrase. In fact, exception phrases can also appear with the determiners each , all, any, and none ofthe, as the sentences in ( 1 s) illustrate.
204
Generalized Quantifiers, Exception Phrases, and L�gicaliry
( I 9) a. Closure under Submodels: IfE' � E and X E II NPII E• then X n E' E I NP II E· b. Closure under Model Unions: IfX n E E II NPII E and X n E' E II NP II E ·· then X n (E u E') E II NPI!EuE' (I 9a) corresponds to anti-persistence (left downward monotoniciry) and supports inferences like (2o). (2o) a. Every/no writer arrived. � b. Every/no poet arrived. ( I 9b) sustains inferences like (2 I ).
The conjunction of (I 9a) and (I 9b) rules our the cases in (1 3). In addition, (1 9a) excludes (22a), and (I 9b) blocks (22b). (22) a. Both/neither/all three student(s) except John arrived. b. At most five students except John arrived. There is, however, a serious problem with (I7). As Hoeksema notes, in a model in which every student except John and n (1 � n) other students arrived, ( I 7) entails that (7a) is true. Similarly, in a model in which no students except for John and n other students arrived, (7b) is true, given the interpretation specified in (1 7). This is clearly the wrong result for both cases. Hoeksema deals with this problem by taking proper names to be referring expressions rather than generalized quantifiers and stipulating that exception NPs of the form NP except PropN are interpreted by the distinct rule given in (23). (23) I NP but a ll � (X � E: X - (a) E !I NPtii E-IaJ) This solution forces us to treat proper names as of a different type than generalized quantifiers (as is the case on the Fregean view). It also requires two distinct rules of interpretation for exception phrase NPs, and so it does not provide a unified account of these NPs. Moreover, it doesn't solve the problem it was designed to deal with. Consider a situation in which a subset Y of the set of students contains five law students and three physics students, and where every student except those in Y participated. In the models for which this situation holds, (I7) implies that both (24a) and (24b) are true. (24) a. Every student except five law students and three physics students participated. b. Every student except five law students participated. But on the desired interpretation of these sentences, (24a) is true and (24b) is false in these models. Therefore, the problem which Hoeksema notes is an
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(2 I) a. Every/no student sings and every/no student dances. � b. Every/no student sings and/or dances.
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instance of a more general difficulty with his definition which is due to the fact that this definition does not specifY the correct connection between the N' set of the quantified NP which an exception phrase modifies and the exception set which corresponds to the NP argument of except. One might try to solve this problem by strengthening ( r 7) to include the requirement that Y is a minimal element of I NP2II , where a minimal set in II NP2II is one which has no non-empty proper subsets.' In fact, this suggestion will not work. Consider the NP most law students. A minimal element of I most law studentsli is a set containing only law students; whose cardinality is the smallest majority of the set oflaw students. On the strengthened version of( r 7), Every student except the majority of law students participated is true iff the set of students minus a set which constitutes the smallest majority of law students participated. Clearly this is not the intended interpretation of the NP or the sentence. Von Fintel (1993) proposes (2 5) as the interpretation of exception phrase NPs. 25. II D(A) except C B ll = t iff C is the smallest set such that B E D(A - C). (2 5) gives a compositional treatment of exception NPs to the extent that it represents the contribution of the exception phrase to the containing NP in terms of the interpretations of the NP argument of except and the NP to which the except phrase applies.8 It captures the first two semantic properties of exception phrases noted at the beginning of this section, if one assumes that B � D(A) (this assumption is analogous to ( r 8) in Hoeksema's analysis). Moreover, if C is defined as Uohn] for (1 3a, c), then (2 5) excludes the exception NPs in these sentences. Consider ( r 3a) for example. If less than five students arrived and John did not arrive, then subtracting Uohn] from the set of students will not make Five students arrived true. If exactly five students arrived and John didn't, then the null set rather than Uohn] is the minimal set which, when subtracted from [students] renders Five students arrived true. Finally, ifJohn and five other students arrived, then there is no unique minimal set which verifies Five students arrived. For any student a who arrived, I arrived I E llfivell (Students [a)). Moltmann points out two significant problems with von Fintel's analysis. First, it does not exclude all non-universally quantified NPs from the set ofNPs with which exception phrases combine. In a case in which John and Mary are the only students and John did not arrive, (2 5) implies that (26a, b) ate true rather than ill-formed. (26) a. *Most students except John arrived. b. *More than half the students except John arrived. Second, it is not clear how this analysis can be extended to exception phrases constructed with quantified or disjunctive NP arguments, as in ( r 6) and (27).
206 Generalized Quantifiers, Exception Phrases, and Logicality
(16) Every student except five law students!John and three physics students/ five computer science students and at most two logic students participated. (27) Every student except John or Mary took a logic course. It does not seem possible to associate a unique minimal set C with the arguments of the exception phrases in these sentences. Finally, Moltmann (1993, 1 995) , like Hoeksema ( 1 99 1 ), takes (connected) exception phrases to be functions from NPs to NPs. The rule which she proposes for interpreting exception phrases relies on the notion of a witness set for an NP, originally defined in B&C. Moltmann employs the slightly modified definition in (28).9
(28) If A is the smallest set for which II NP II is conservative, then W is a wimess Thus, for example, UohnJ is the only witness set for llfohnll , Uohn, mary] is the only wimess set for l John and Maryll . UohnJ,(mary], and Uohn ,mary J are the wimess sets for llfohn or Maryll and any set containing five students (and nothing else) is a witness set for llfive studentsll . Moltmann also stipulates that an appropriate extension M' of a model M for an NP ofthe form NP1 except NP2 is an extension of M in which (i) II NP1 II is defined in M ' if it is defined in M, and (ii) II NP2II M . = II NP 2II M· She proposes (29) as the interpretation of exception phrase NPs, where w(ll NPII ) is the set of witness sets for II NPII . 1 0
(29) ( ll except ii M(II NP211 M))(II NP I II M) II NPI II MJ,
=
u(V ' E w(II NP211 M)) (V - V': v E
if for every appropriate extension M' of M, for every V E II NP 1 II M ', and for every V ' E II NP2II M ', V' <;;;;; V. = u(V ' E w(II NP211 M)) (V v V': v E I NP I II MJ, if for every appropriate extension M' of M, for every V E II NP 1 II M ' , and for every V ' E II NP2II M ', V' n V 0. undefined otherwise. =
=
(29) specifies the denotation of an exception phrase of the form NP1 except NP2 as (i) the set of sets formed by subtracting a witness set for NP2 from each of the sets in II NP1 II if each of the witness sets is a subset ofevery set in II NP1 II , or (ii) the set of sets formed by adding a wimess set for NP2 to each of the sets in II NP1 II , when the intersection of each witness set and any set in II NP1 II is empty. The condition that every witness set for NP1 be either included in each set of II NP1 II (the first case) or totally excluded from each set in II NP2II expresses the requirement that exception phrases apply only to GQs which satisfy what Moltmann refers to as the Homogeneity Condition , stated in (3o), for every element w( II NP2II ).
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set for II NP II . iffW <;;;;; A and W E II NP II ·
Shalom Lappin 2.07
(30) I NPII satisfies the Homogeneity Condition with respect to a set C iff, for every X E IINPII , either C � X or C n X = 0.
(7)
Every student except John arrived. b. No student except John arrived. a.
If II arrivedll is an element of this set, thenJohn is in the complement of I arrivedll . The subject of (7b) is an instance of case (ii), and its denotation is the set of all sets true of no student except John. If I arrivedll is an element of this set, then John is in the complement of the set of things which did not arrive. The Homogeneity Condition, which is built into 29, excludes the ill-formed exception NPs in (I 3). Moststudents exceptjohn, for example, is ruled out because the denotation of most students includes both sets which contain John and sets which do not, and similarly for the other ill-formed NPs in (I 3). While the Homogeneity Condition will filter out most NPs to which exception phrases cannot apply, it will allow certain unwanted cases, like the NP subjects of (22a). (22) a. *Both/neither/all three student(s) except John arrived.
II both students II , II neither students I , and I all three students I satisfy ( 3 o) with respect to any predicate set. Moltmann also postulates a minority condition on exception NPs, which states that for any model M, (II exceptii M(II NP2II M))(II NP1 IIM) is defined only if, for every V E w(II NP2II)M, l A - VI > V in M, where A is the smallest set for which II NP111 is conservative. This condition will exclude NPs of the form neither N' or both N' from the range of exception phrase modifiers. However, it will not block NPs of the form all n N' except NP. 1 1 Moreover, it is not obvious that this condition is correct. Consider a situation in which there are 3 so seats in Parliament, Labour has 200 seats, the Conservatives I OO, and the Liberal Democrats so. Assume that all and only the Labour MPs support a given bill. It would still seem to be the case that 3 I is true (and appropriate) in this situation. (3 I) Everyone except the Labour MPs opposed the bill.
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Given (29), every student except five law students denotes the set of every set which contains all students minus the elements of a wimess set of five law students. No student exceptfive law students denotes the set of every set containing no students except for the elements of a wimess set of five law students. (29) provides a compositional representation of exception phrase NPs. Moltmann proves a theorem stating, in effect, that (29) entails the first semantic property of exception NPs. The second property follows directly from (29). Thus (7a), for example, where the subject NP is an instance of case (i), implies thatJohn did not arrive by virtue of the fact that every student exceptjohn denotes the set of sets true of all students except John.
208 Generalized Quantifiers, Exception Phrases, and Logicality
Therefore, the exception NPs in (22a) pose a problem for Moltmann's analysis. 1 2 3 .2
An alternative account ofexception NPs
(32) R is total iff (i) R - �. or (ii) for any two sets A, B, R{A, B) iff A n B
�
0.
According to (32), R is total iff it imposes a condition of inclusion or exclusion between two sets, and nothing more. Let NP2 be the NP to which the exception phrase except(NP1) applies, and assume that II NP2II = {X � E: R{A, X)). I restrict the domain of the function which an exception phrase denotes by requiring that it apply only to NP arguments for which R is total in every model M such that the value of the NP is defined in M. For any set X, let X' be the complement of X. We can specify the interpretation of exception phrase NPs by the rule given in (3 3). {33) { ll except ii {IINPtii )){II NPzll ) - {X � E: R{Nem, X), where II NPzll = {X � E: R{A, X)), and 3S{S e w(II NP1 I ) & S � A & Nem = A - S & R(S, X'))), ifR is total and A i' 0. = undefined otherwise. (3 3) requires that the restriction set of the NP to which the exception phrase applies be non-empty in order for the denotation of the entire exception phrase NP to be defined. Therefore, on (3 3) both Every unicorn except a green one appeared in the garden and No unicorn except for a green one appeared in the garden are undefined for truth-value, which seems to be the desired result.O If we apply (3 3) to every student exceptfive law students, we obtain (34a). The interpretation of (16), with the selection of except five law students as the exception phrase modifying the subject NP, is given in (34b). (34) a. ( ll exceptii {{X � E: I Law_students (") X I � s})){{X � E: Students � X}) - {X � E: Students•em � X, where 3S(S E w({X � E: I Law_students n X I � s}) & s � Students & Studentsrem = Students - s & s � X'))).
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The account of exception phrase NPs which I propose is in the spirit of the analyses proposed in Hoeksema (199 1 ) and Moltmann, but it differs sig nificantly from these treatments in the details of implementation. I follow Hoeksema and Moltmann in taking exception phrases to be modifiers of NP. I adopt Hoeksema's general strategy of characterizing the denotation of an exception phrase NP in terms of a remnant set Arem obtained by subtracting a set associated with the NP argument of except from the restriction set A of the NP to which the exception phrase applies. I use Moltmann's concept of a witness set to specify the set whch is subtracted from A. I define a total relation R between two sets as in (32).
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b. I every student except five law students participated I - t iff Student"em s;;; {a: a participated}, where 3S(S E w({X s;;; E: ! Law_students n X I ;?; s}) & s s;;; Students & Studentsrem - Students - s & s s;;; {a: a participated}')).
(I 3) a. *Five students exceptJohn arrived. b. *Most MPs except the Tories supported the bill. c. *Mary spoke to many people exceptJohn. d. *Not many students except five law students participated. (3 3) avoids the problem which Hoeksema's ( 1 99 1 ) analysis encounters. The requirement that S, a set subtracted from A to yield the remnant set A•em, be a witness set of II NP1 11 imposes a minimality condition on S. In (34a, b), for example, S contains only five law students. Therefore, in situations where (24a) is true, (24b) is not. (24) a. Every student except five law students and three physics students participated. b. Every student except five law students participated. Also, unlike Moltrnann's (29), (33) rules out the subject NPs in (22a). (22) a. *Both/neither/all three student(s) except John arrived. The determiners of the NPs to which except John applies do not denote total relations by virtue of the fact that they impose cardinality conditions on the
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(3 3) provides a unified compositional representation of exception phrase NPs. It also captures the three central semantic properties of these NPs. First, given this definition, both (7a) and (7b) imply that John is a student. This implication holds by virtue of the fact that the witness sets for II NP1 11 , the argument for the exception phrase, which render the existential assertion In (33) true are subsets of the N' set of the NP to which the exception phrase applies. Second, it sustains the inference from (7a) to the assertion that John did arrive, and the inference from (7b) to the statement that John did not arrive. These inferences hold because of the requirement that the same total relation R which holds beween the remnant set Nem and the VP set, also hold for the witness set S for I NP1 11 in terms of which Nem is defined and the complement of the VP set. Finally, in (33) the domain of exception phrase functions is restricted to generalized quantifiers whose determiners denote total relations between their N' sets and the VP sets of the predicate. Therefore, (33) correctly excludes the application of exception phrases to NPs whose determiners are not universal, like those in ( 1 3 ).
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Generalized Quantifiers, Exception Phrases, and Logicality
(3 5) Every mother and every father except the teachers joined the PTA. It seems that when exception phrases modify coordinate NPs, they are restricted to uniform conjunctions of positive or negative universally quantified NPs.
( 36) a. *Every mother and no/several/most fathers except the teachers joined b. c. d. e.
the PTA. *Every mother or every father except the teachers joined the PTA. No mother and no father except the teachers attended the meeting. *No mother and every/several/most fathers except the teachers attended the meeting. *No mother or no father except the teachers attended the meeting.
The denotation of an NP of the form every(A1 ), , and every(Ak) (I :s;; k) is ri'-111 every (�)ll (the intersection of the denotations of each of the NP conjuncts). Similarly, the denotation of an NP of the form no(A 1 ), , and no(Ak) (l :s;; k) is ri'-1 1 no(�) l · For example, II every mother and everyJatherll is the intersection of the set of sets containing all mothers and the set of sets containing all fathers. •
•
•
•
•
•
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restriction set of the NP denotation. Therefore, the function denoted by excep tion phrases are not defined for these NP denotations. It must be conceded that 3 3 restricts the range of exception phrase functions to universally quantified NPs by explicitly stipulating that this range is limited to NPs which exhibit the defining semantic property of universal GQs. However, this requirement is not more stipulative than the conditions which Hoeksema and Moltmann invoke to rule out inappropriate arguments for exception phrase modifiers. In both the latter theories the relevant condition does not follow from the proposed interpretation of exception phrases, but must be independently postulated as an additional constraint on the rule of interpretation. The major difference between the analyses of Hoeksema and Moltmann on one hand and the account proposed here on the other is that while the latter formulates the stipulation governing the range of exception phrases directly in terms of the defining property of universal NPs, Hoeksema and Moltmann attempt to derive the restriction indirectly from equally stipulative conditions which rely on alternative semantic properties. In fact, it is not clear that the distribution of exception phrase modifiers follows from deeper semantic properties than those invoked in (3 3). In addition to empirical adequacy, the proposed distributional constraint at least has the virtue of specifying the intended range of exception phrase functions directly and transparently in terms of the defining semantic property of their arguments. Moltmann (1993) points out that exception phrases can also apply to certain coordinate NPs. In (3 5), for example, except the teachers can be understood as modifying the conjoined NP every mother and everyfather.
Shalom Lappin 2 I I
But this set is identical to the set of all sets containing the union of the set of mothers and the set of fathers. Similarly, the denotation of no mother and no father is the set of all sets whose intersection with the union of the set of mothers and the set of fathers is empty. Therefore, the identities of (3 7) hold. (37) a. ll every(At), . . ., and every(AJ II - {X s:;;; E: (A t u . . . u Ak) s:;;; X) b. II no(At), . . ., and no(AJ II - {X s:;;; E: (At u . . . u AJ n X = 0)
(38) a. Every boy danced with every girl, except John with Mary. b. No student talked to any professor except two law students to one computer science professor. (3 8a) asserts that for every ordered pair (a, b) in which a is a boy, b is a girl, and (a, b) i' �. m), a danced with b, and j did not dance with m. Similarly, (3 8b) implies that there is a set S = {(a, b): Law_Student(a) & CS_Professor(b) & tal ked_to(a, b) & i{x: x - a)I - 2 & I {y: y - bJI - 1 J that such S � (Students x Profes sors), and for every ordered pair (a, b) in (Students x Professors) - S, a did not talk to b. The resumptive GQ which corresponds to (every boy, every girl) in (38a) is ll everyii (Boys x Girls), which receives the interpretation given in (39). (39) ll every ii (Boys x Girls) - {R s:;;; E x E: (Boys x Girls) s:;;; RJ The interpretation of the polyadic generalized quantifier associated with (John ,Mary) is specified in (4o). (40) II(John,Mary)ll .;.. {R s:;;; E x E: IUohn ll ({x:II Mary l ({y: R(x,y)J) = t)} = t) The witness set for the polyadic quantifier defined in (40) is {�,m)J. If we apply the exception phrase function II except li ({R s:;;; E x E: IUohn ll ({x: IIMary ll ({y: R(x,y)J) = t)} - t)} to the resumptive quantifier defined in (39), then, by (3 3), we obtain (4 1). (4 1 ) ( ll except ii ({R s:;;; E x E: IUohn ll ({x: II Mary ll ({y: R(x,y)J) = t)} - t)})({R s:;;; E x E: (Boys x Girls) s:;;; R)} = {R s:;;; E x E: (Boys x Girls)'em s:;;; R, where 3S(S E w({R s:;;; E x E: IUohn ll ({x: II Mary ll ({y: R(x,y)J) - t)} - t)} & S s:;;; (Boys x Girls) & (Boys x Girls)'em - (Boys x Girls) - S & S s:;;; R'))).
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Given (37), the interpretation of exception phrases specified in (3 3) covers (35) and (36c), while excluding the ill-formed cases of (36). It is important to note that the fact that exception phrases can apply to con joined NPs provides strong motivation for treating them as modifiers of NP rather than as constituents of complex determiners. Moltrnann ( 1 993, 1 995) also observes that exception phrases can modify uniform sequences of universally quantified NPs which are interpreted as resumptive quantifiers, as in (38). t 4
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Generalized Quantifiers, Exception Phrases, and Logicality
(41 ) produces the interpretation of (38a) given in (42), which represents the desired reading. (42) II every boy danced with every girl, except John with Mary\\ = t iff (Boys x Girls)'em � {(a,b): danced_with(a,b), where 3S(S E w({R � E x E: JUohn ll ({x: 1\ Mary\\({y: R(x,y))}) - t)) = t) & S � (Boys x Girls) & (Boys x Girls)'em - (Boys x Girls) - S & S � {(a,b): danced_with(a,b))')). Similarly, the GQ which corresponds to (no student, no professor) in (38b) is II noii(Students x Professors), which is interpreted as in (43). (43) 1\ no \\ (Students x Professors) = {R � E x E: (Students x Professors) n R = 0)
(44) 1\ (two law students,one computer science professor)\\ = {R � E x E: \\ two law students\l ({x: \l one computer science professor\\ ({y: R(x,y)) - t))} = t) A witness set for the polyadic quantifier defined in (44) is a set W of ordered pairs (a,b) such that a is a law student, b is a computer science professor, and there are two distinct values for a and one value for b. The application of the function which the exception phrase in (38b) denotes to the resumptive quantifier specified in (43) yields (45).
(45) ( \lexcept\\ ({R � E x E: I\ two law students\! ({x: I/ one computer science professor/l ({y: R(x,y))} - t)) = t)}) ({R � E x E: (Students x Professors) n R = 0)} {R � E x E: (Students x Professors)'em n R = 0, where 3S(S E w({R � E x E: 1/ two law students 1/ ({x: II one professor II ({y: R(x,y))} = t)} = t)} & S � (Student x Professors) & (Students x Professors)'em = (Student x Professors) - S & S n R' = 0)) (45) correctly generates (46) as the interpretation of (3 8b). (46) II no student talked to any professor except two law students to one computer science professor// = t iff (Students x Professors;em n {(a,b): talked_to(a,b)) = 0, where 3S(S E w({R � E x E: // two law students l/({x: /l one computer science professor l/ ({y: R(x,y))} - t)} = t)} & S � (Student x Professors) & (Students x Professors)'em = (Student x Professors) - S & S n {(a,b): talked_ro(a,b))' - 0) Therefore the rule for interpreting exception NPs given in ( 3 3) generalizes directly to cases in which an exception phrase modifies an NP sequence which is taken as a universal resumptive quantifier.
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The interpretation of the polyadic generalized quantifier associated with (two law students, one computer science professor) is (44).
Shalom Lappin 2 1 3
4· EXCEPT I O N P H RASES A N D L O G I CAL I TY 4.1
The logically heterogeneous character ofexception NPs
Let us return to the question of whether logicality provides a criterion for distinguishing different categories and types of NPs in natural language. Exception phrase NPs are heterogeneous with respect to logicality. An excep tion phrase NP is a logical GQ iff it is of the form every A except det A , and det is a logical determiner. This is not the case for other exception NPs. Consider the contrast between (47a), on one hand, and (47b, c) on the other.
Let W in (48) be a witness set S for the argument of except which satisfies the condition for S specified in the existential clause of (3 3). Students
Participated
As (49a) indicates, it is possible to characterize the interpretation of every student exceptfive (students) solely in terms of the cardinality values a, d, and e, where, crucially, W can be any subset of Students with a cardinality of (at least) s. Therefore, the truth-value of (47a) remains constant for any permutation of the elements of the predicate set Participated with the elements of another set which respects the cardinality ofParticipated and its intersection with the set of Students. This is not the case for every student except five law students or every
student exceptjohn .
(49) a. II every student except five (students) participated II = t iff a = o, d = o, & e � s (W any subset of Students with a cardinality of s ) b. II every student except five law students participated II = t iff a = o, d - o, & e � s (W a set of law students with a cardinality of s) c. ll every student except John participated ll - t iff a - o & W Participated = UJ.
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(47) a. Every student except five (students) participated. b. Every student except five law students participated. c. Every student except John participated.
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(so) a. A representative of every city attended the meeting. b. A representative of every city except two (cities) attended the meeting. c. A representative of every city except Migdal HaEmek attended the meeting. Similarly, scope ambiguity is present in all of the sentences in (s I ). (s I ) a. No student attended a logic course. b. No student except five (students) attended a logic course. c. No students except two computer science students attended a logic course. Moreover, as the cases in (s2) and (S3) show, both logical and non-logical exception phrases impose a bound variable reading on the pronouns which they bind. (s2) a. b. (s 3) a. b.
Every student except one (student) submitted his paper. Every student except John submitted his paper. No journalist except one checked his facts. No journalist except Mary checked her facts.
The defining syntactic and semantic properties of exception phrase NPs do not appear to be sensitive to logicality. This provides motivation for the claim that these NPs form a unified syntactic subcategory of the category NP and a single semantic subtype of the type GQ. As the property of logicality is orthogonal to this type, it does not provide the basis for distinguishing among different semantic types of NPs. This conclusion is incompatible with the Logicality Thesis, given the logically heterogenous character of exception phrase NPs. It is, however, a consequence of the generalized quantifier view on
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Given (49), if we substitute a set B for Participated which preserves the cardinal values a, c, d, and e but permutes elements of Students•em n Participated not contained in the set of law students with elements of W (so that the permutation verifies Every student exceptfivephysics students B, for example), then the truth-value of (47b) changes. Similarly, if we substitute a set B for Participated which preserves the cardinal values a, c, d, and e but permutes john in W - Participated with bill in Students•em n Participated, the truth-value of (47c) is altered. However, both logical and non-logical exception phrase NPs display the same properties which May and Higginbotham initially cited as motivation for representing quantified NPs as operator-variable structures at LF. Specifically, both variants of exception phrase NPs exhibit the same relational scope properties as the logical GQs from which they are derived. Thus, for example, the wide scope reading of the PP complement relative to a representative is preferred in each of the sentences in (so).
Shalom Lappin
21 S
which NPs in general constitute a unified syntactic category and corresponding semantic type. 4.2
Exception phrase NPs and the deductive treatment ofnatura/ language quantifiers
(54) X1, � f- A iff .n[XI), . . ., .n[Xn] f- .n[A] for each permutation Jr of the underlying universe of models or states. •
•
•
This constraint effectively imposes the requirement of logicality on the generalized quantifiers whose interpretations are given proof-theoretically. As we have seen, the set of generalized quantifiers which are generated by the application of exception phrase functions to universal NPs is not uniform with respect to logicality. Certain inference patterns will hold under all permuta tions for some exception NPs but not for others. Thus, for example, logical exception NPs will support inferences of the form given in (55), which is illustrated in (56). (55) Every/no A except n A's B. The number of As which B is equal to the number of As which C. => Every/no A except n As C. (56) Every/no student except five (students) sings. The number of students who sing is equal to the number of students who dance. => Every/no student except five (students) dances. Comparable inferences do not go through with non-logical exception NPs, like
every student exceptfive law students.
(57) Every/no student except five law students sings. The number of students who sing is equal to the number of students who dance. '*> Every/no student except five law students dances. It follows that the GQs denoted by exception phrase NPs cannot be uniformly modelled by a proof-theoretic system which satisfies the condition
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Recently, several proof-theoretic systems have been proposed for characteriz ing the meanings of natural language expressions through deductive procedures rather than model-theoretic interpretation. 1 5 In general, these sys tems specify the contribution of an expression to the meaning of a sentence in terms of the set of inferences which the expression licenses. Van Benthem ( I 99 I ) suggests that a proof-theoretic account ofgeneralized quantifiers should satisfy the general constraint that the notion of entailment which it specifies is invariant under permutation in the sense defined in (54).
2 1 6 Generalized Quantifiers, Exception Phrases, and Logicality
of invariance under permutation. To the extent, then, that a proof-theoretic representation of GQs is a logical system that satisfies (54), it will not be able to accommodate the full set of quantified NPs which occur in natural language. Exception phrase NPs pose a serious challenge for a program that seeks to develop a proof-theoretic characterization of the full range of generalized quantifiers corresponding to quantified NPs in natural language.
5 CONCLUSION
Acknowledgements
Earlier versions of this paper were presented at the SOAS Workshop on Deduction in Natural Language, SOAS, University of London in March 1 994, the Semantics Seminar at the Conference of the Linguistics Association of Great Britain, Middlesex University, September 1 994, and the Bar-Ilan Symposium on the Foundations of Artificial Intelligence, Bar Ilan University, June 1 99 5 · I am grateful to the participants of these conferences for their comments. I would like to thank Ruth Kempson, Friederike Moltmann, and rwo anonymous
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I have considered the debate between the Fregeau and generalized quantifier approaches to NPs in light of the properties of exception phrase NPs, which constitute a subset of the set of quantified NPs. On May's version of the Fregeau view, logicality is the basis for partitioning NPs into two distinct syntactic cate gories and associated semantic types. At the level of syntactic structure which determines the category-type correspondence, logical NPs are represented as operator-variable chains while non-logical NPs appear in situ in argument position. On the GQ view, logical and non-logical NPs are elements of a unified syntactic category and correspond to a single semantic type. The dis tinction between logical and non-logical NPs (as well as the difference between quantified and non-quantified NPs) is orthogonal to this category and its asso ciated type. I have examined four recent analyses of exception phrase NPs and found significant difficulties with each of them. The alternative account proposed here avoids these difficulties and captures the major semantic properties of exception NPs. On this account, exception NPs are heterogeneous with respect to logicality. However, both logical and non-logical elements of this subset exhibit the scope and semantic binding properties of other quantified NPs. May and Higginbotham invoke these properties as an important part of their case for representing quantified NPs as operator-variable structures at LF. The fact that exception phrase NPs are non-uniform for logicality but behave like other quantified NPs in connection with scope and semantic binding provides motivation for the generalized quantifier approach to the syntax and semantics ofNPs in natural language.
Shalom Lappin 2 1 7 referees for helpful criticism and advice. Finally, I am particularly grateful to Jaap van der Does for extensive comments on a previous draft of this paper. Received: 07.I 1 .9 5 Revised version received: 03.05.96
SHALOM LAPPIN
School ofOriental and African Studies University ofLondon Thornhaugh Street, Russell Square London WC1H OX6 UK e-mail: [email protected].
N O TES
• . •
• • •
• • •
M', then detM (A1,
. . ., Ak)·
• • •
, Ak) - detM. (A1,
I will follow B&C, K&S, and Wester stahl in assuming that all natural language determiners denote conservative func tions. I will also adopt Westersdhl's suggestion that natural language deter miner functions satisfy the Extension condition. Given these assumptions, the distinction between logical and non-logi cal natural language determiner functions depends upon the property of invariance under isomorphic structures defined on E. 6 See Hoeksema ( I99 I ), von Fintel (I99 3), and Moltmann (I99 3, I995) for discus sions of these properties. Moltmann ( I 99 5) provides detailed criticisms of the theories proposed in Hoeksema (198 7, I989), and von Fintel (I99 3)· 7 I am grateful to Jaap van der Does for suggesting this possibility to me. 8 Von Fintel considers two possibilities for the syntactic category and semantic type of exception phrases. The first is that they are modifiers of determiners. The second is that they are functions from common nouns to higher type common nouns, with the latter being functions from determiners to NPs. He does not decide between these alternatives. I will set this issue aside, as it is not directly relevant to the problems which attach to his pro-
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1 See Chomsky ( 1 9 8 1 , 1986, 1992 and 1 994) for this model of syntax. 2 See May (I985, I989) for a discussion of the relation between the syntactic scope of an NP at LF and the set of possible scope interpretations which its syntactic scope allows. See May ( I 99 I, pp. 3 5 I -5) for discussion of the Logicality Thesis view of LF. 4 See, for example, Montague (I974), Barwise & Cooper ( I 98 I ) (B&C), Cooper ( I 98 3), Keenan & Stavi (K&S), and van Benthem (I 986) for different versions of the GQ approach. May and Higgin botham provide independent syntactic and semantic arguments for incorporat ing QR and the level of representation which it defines into the grammar. See Lappin (I99 I ) for a critical discussion of some of these arguments and a defence of the GQ account of the semantics of NPs. See May ( I 99 I ) for a response to some of the points raised in Lappin (I 99 I ). These conditions are specified for k-place (I � k) determiner functions in (i) and (ii), respectively (see B&C, van Benthem, Keenan & Moss (I985), and K&S for discussions of conservativity). (i) A k-place determiner function det is conservative iff B E det (A1, , Ak) <> (A1 u . . . u Ak) n B E det (A1, , AJ. (ii) A k-place determiner function det satisfies Extension iff for any two models M and M ', if A1, Ak � M �
2 I 8 Generalized Quantifiers, Exception Phrases, and Logicaliry posed semantics for exception phrase NPs. 9 The notion of conservativiry can be extended from determiners to NPs by specifying that �NPII is conservative for the set A iff for every X E IINPII, X '"' A E IINPII. I O This definition is intended to apply to NPs formed by applying an exception phrase to a quantified NP interpreted as a retricted unary quantifier. Moltmann generalizes the definition to cases m which exception phrases apply to resumptive quantifiers, as in (i).
I d iscuss cases of this kind in section 3.2. I I Moltmann (p.c.) points out that (i)b IS better than (i)a.
(i) a. ?all 100 students except John b. *all three students exceptJohn
A possible explanation for the contrast between these cases is that with lower cardinaliry values for n, all n functions as a determiner, while for higher values n is treated as a separate appositive element which is not part of the determiner. On the latter reading, all n N ' is interpreted as all N', and, incidentally, there are 1 oo N ' s. I 2 Moltmann (p.c.) suggests that the NPs in (22a) could be ruled out by a pragmatic constraint which prevents the application of exception phrases to NPs whose deter miners are both universal and impose a cardinaliry condition on their N ' sets. Even if such a constraint can be motivated, the result would be an
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(i) a. Every boy danced with every girl, except John and Mary. b. No student talked to any professor except two law students to one computer science professor.
undesirable distinction between semanti cally ill-formed exception NPs, like those in {I 3), and pragmatically excluded cases, like those in (22a). In fact, the NPs in both sets of examples seem to be unacceptable to the same degree. If the NPs in (22a) violate a pragmatic but nor a semantic constraint, it should be possible to con struct possible situations in which the constraint is overridden or does not hold. However, the NPs in (22a), like those in {I 3). would seem to be unacceptable in all possible situations. I 3 I am grateful to an anonymous reviewer for pointing out the problem of null restriction sets for NP arguments of exception phrases. 1 4 See May ( I 989) for a discussion of resumptive quantifiers. See Keenan (I987) and van Benthem ( I 989) for discussions of polyadic quantifiers. I s See, for example, Kempson & Gabbay {I99 3). and Kempson (I996) for outlines of a general framework for interpretation by natural deduction. Van Lambalgen (I99 I) suggests rules of natural deduction for several unary generalized quantifiers. Van Benthem {I99 I ) discusses some of the issues involved in developing a proof theoretic account of generalized quantifi ers. Dalrymple et a/. ( I 994) presents a set of deductive procedures for representing quantifier scope relations within the framework ofLFG. The system makes use of Girard's ( I 987) linear logic. However, unlike van Lambalgen's rules, it does not attempt to express the semantic content of quantified NPs in proof-theoretic terms. Instead it offers a deductive alternative to interpretation through compositional function-argument appli cation in a higher-order rype system.
Shalom Lappin 2 1 9
RE F E RE N C E S
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Chomsky, N. (1994), Bare Phrase Structure, MIT Occasional Papers in Linguistics, MIT, Cambridge, MA Cooper, R. ( 1 98 3), Quantification and Syntactic Theory, Reidel, Dordrechr. Dalrymple, M., Lamping, J., Pereira, F. and Saraswat, V. ( 1994), 'A deductive account of quantification in LFG', MS Xerox Pare, Palo Alto, CA and AT&T Bell Labora tories. Murray Hill, NJ. von Finrel, K. ( 1993), 'Exceptive construc tions', Natural Language Semantics, I, 12348. Girard, Y.-Y. ( 1987), 'Linear logic', Theoretical Computer Science, 45, 1 - 1 02. Higginbotham, J. (1985), 'On semantics', Linguistic Inquiry, I 6, 547-94. Higginbotham, J. & May, R ( 198 1), 'Ques tions, quantifiers, and crossing', The Linguistic Review, I, 4 1 -79. Hoeksema,]. ( 1 987), 'The logic of exception', .
Proceedings ofESCOL, 4,
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Hoeksema,]. ( 1989), 'The semantics of excep tion phrases', in L. Torenvliet & M.
Srokhof(eds), Proceedings ofSeventh A mster dam Colloquium, ITLI, Amsterdam. Hoeksema,]. ( 1 99 1), 'The semantics ofexcep tion phrases', in J. van der Does & J. van Eijk (eds), Generalized Quantifiers and Applica tions, Dutch Nerwork for Language, Logic, and Information, Amsterdam, 245-74. Keenan, E. ( 1987). ;Unreducible n-ary quan tifiers in natural language', in P. Garden fors (ed.), Generalized Quantifiers: Linguistic and Logical Approaches, Reidel, Dordrecht, 1 09-50. Keenan, E. and L. Moss ( 1 995), 'Generalized Quantifiers and the Expressive Power of Natural Language' in J. van Bentham and A. ter Meulen (eds.), Generalized Quantifiers in Natural Language, Foris, Dordrecht, 73-124. Keenan, E. & Stavi, J. ( 1986), 'A semantic characterization of natural language determiners', Linguistics and Philosophy, 9, 253-326. Kempson, R. (1996), 'Semantics. pragmatics, and natural language interpretation', in S. Lappin (ed.), The Handbook ofContemporary Semantic Theory, Blackwell, Oxford, pp. 561-98. Kempson, R. & Gabbay, D. ( 1993), 'How we understand sentences. And fragments too?' in M. Cobb (ed.), SOAS Working Papers in Linguistics and Phonetics, J, 259-336. van Lambalgen, M. (199 1), 'Natural deduc tion for generalized quantifiers', in J. van der Does & J. van Eijk (eds), Generalized Quantifiers and Applications, Dutch Network for Language, Logic, and Infor mation, Amsterdam, 143-54. Lappin, S. (199 1 ), 'Concepts oflogical form in linguistics and philosophy', in A. Kasher (ed.), The Clwmskyan Turn, Blackwell, Oxford, 30D- 3 J. Lindstrom, P. ( 1966), 'First order predicate logic with generalized quantifiers', Theoria, 32, 1 72-85. May, R ( 1 985), Logical Form: Its Structure and Derivation, MIT Press, Cambridge, MA.
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Barwise, J. & Cooper, R ( 1 981), 'Generalized quantifiers and natural language, Linguis tics and Philosophy, 4, 159-2 19. van Benthem, J. (1986), Essays in Logical Semantics, Reidel, Dordrecht. van Benthem, J. ( 1 989), 'Polyadic quantifica tion', Linguistics and Philosophy, 12, 43764. van Benthem, ]. ( 199 1), 'Generalized quanti fiers and generalized inference', in J. van der Does & J. van Eijk (eds), Generalized Quantifiers and Applications, Dutch Nerwork for Language, Logic, and Infor mation, Amsterdam, 1- 1 3· Chomsky, N. (1981), Lectures on Government and Binding , Foris, Dordrecht. Chomsky, N. (1986), Barriers, MIT Press, Cambridge, MA Chomsky, N. ( 1 992), A Minimalist Programfor Linguistic Theory, MIT Occasional Papers in Linguistics, No. 1 , MIT, Cambridge,
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( I 989), 'Interpreting logical form', 12, 387-4 3 5. May, R. (I 99 I ), 'Syntax, semantics, and logical form', in A. Kasher (ed.), The Chomskyan Turn, Blackwell, Oxford, 3 3 4-59Molrmann, F. (I 99 3). 'Resumptive quantifiers in exception sentences', in H. de Swart, M. Kanazawa, & C. Pinon (eds), Proceedings of
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University Press, New Haven, CT, 247-70. Mostowski, A. {I9S7). 'On a generalization of quantification', Fundamenta Mathematicae, 44. I 2-3 6. Sher, G. ( 1 99 1 ), The Bounds of Logic, MIT Press, Cambridge, MA. Sher, G. ( 1 996), 'Semanrics and Logic' in S. Lappin (ed.), The Handbook ofContemporary Semantic Theory, Blackwell, Oxford, 5 1 1 -37· Westerst:ihl, D. ( 1 9H9), 'Quantifiers in For mal and Natural Languages' in D. Gabbay and F. Guenthner (eds.), Handbook ofPhilo sophical Logic, Vol. IV, Reidel, Dordrechr, 1-1 3 I .
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Molrmann, F. ( I 99S). 'Exceprion senrences and polyadic quantification', Philosophy and Linguistics, 18, 223-Xo. Monrague, R. (I 97�). 'The proper rrearmenr of quanrificarion in ordinary English', in R. Monrague, Formal Philosophy (edited by
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© Oxford University Press 1 9'}6
Meaning and Use of not . . . until
HENRIETTE DE SWART Department ofLinguistics, Stanford University
Abstract
I I NTROD U C T I O N I .I
Scope, polarity and lexical composition
In temporal semantics, a distinction is made between durative or atelic sentences ( I ) and non-durative or relic sentences (2):
( I ) a. Susan loves Paul. b. Andrew swam. (2) a. Eve drew a circle. b. Mary reached the summit. Vendler (I957) provides a more fine-grained classification and distinguishes between states (1a) and activities ( I b), and accomplishments (2a) and achieve ments (2b). 1 In this paper I will ignore the distinction between accomplish ments and achievements and taken them together as the class of event predicates. Following Bach ( I 986), I will use the term 'eventuality' to generalize over states, activities, and events. A number of time adverbials are sensitive to the aspectual character of the sentence they combine with. Among others, this is true for time adverbials and
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Time adverbials introduced by until impose restrictions on the aspectual class of the main clause they combine with: they only combine with durative sentences. In negative sentences, the situation is more complex. The question arises whether negative sentences are durative, or whether there is a separate use of until as a negative polarity item. In this paper, I discuss the three treatments of not . . . until that are characterized in the literature as the scope analysis, the ambiguity thesis and the lexical composition approach. I work out the interpretation of the three approaches in an event-based semantics, and argue that they are truth-conditionally equivalent in sentences containing an explicit negation. Furthermore, they generate the same pragmatic implicatures. A separate negative polarity use of until is motivated by sentences containing NPI-licensers different from explicit negation, though. The observation that the scope analysis, the ambiguity thesis and the lexical composition approach are semantically and pragmatically equivalent in sentences containing an explicit negation helps us describe the similarities and differences between the expression of exclusion of a range ofvalues on the time axis in a variety of languages.
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temporal clauses introduced by until. Until only combines with durative sentences containing a state or activity description: (3) a. b. c. d.
Susan wrote until midnight. Susan wrote letters until midnight. Susan didn't write a letter until midnight. *Susan wrote a letter until midnight.
(4) a. Susan doesn't have a red cent. b. No one lifted a finger to help me. c. If any of you ever goes to Paris, you should come to visit me. d. This is more money than anyone would have expected to get. e. This is the best movie I have ever seen. £ George is too lazy to do anything. One of the points of discussion in the interpretation of not . . . until concerns the ambiguity of sentences like ( s ):
( s ) The princess did not sleep until nine o'clock. On one reading of the sentence, ( s ) means that the princess did not sleep all the time until nine o'clock (that is, she woke up earlier than nine). Alternatively ( s ) can be used to claim that there was not a situation of the princess being asleep until nine o'clock (i.e. until nine o'clock, she was awake). On this reading, there is a strong suggestion that the princess fell asleep at or shortly after nine.2 Defenders of the one until-theory like Smith ( 1974) and Mittwoch (1977) claim that the ambiguity of sentences like ( s ) is due to a difference in scope. If negation can take either wide or narrow scope with respect to the until-phrase, the two readings can be represented as in (6): (6) The princess did not sleep until nine o'clock. a. -.(until nine o'clock (the princess slept)) b. (until nine o'clock (-.(the princess slept)))
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The fact that negative sentences combine with until has been taken as an argument that negation is an aspectual operator, which yields durative sentences as output. Under this assumption, the contrast between (3c) and (3d) is explained as a difference in aspectual character between non-durative sentences and their durative negative counterpart. Alternatively, it has been suggested that there are two untils: one the well-known durative until and the other a punctual until which only shows up as a negative polarity item (NPI). In this view, (3d) is out because the sentence is not durative, and does not contain an NPI-licenser. Negative polarity items are expressions like any, ever, lift a finger, which only show up in the context of negation, negative quantifiers, if clauses, comparatives, superlatives, too , and the like (c£ Ladusaw 1 979):
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(7) a. The princess didn't wake up until nine. b. The princess didn't wake up before nine. c. The princess woke up at nine (or shortly thereafter). I assume that Karttunen does not take the commitment to (7c) to be part of the assertion, but views it as an implicature. This seems reasonable in view of the fact that the implicature can be cancelled (as in (8a)) or suspended (as in (8b)) (similar examples are in Horn, 1 972):3 (8) a. She said she wouldn't come until Friday. In the end, she didn't come at all. b. I won't leave until Friday, if at all.
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The combination of wide scope negation with durative until in (6a) gives us the interpretation in which it is not the case that the princess slept all the time until nine o'clock, but she woke up earlier. The narrow scope of negation with respect to durative until means that, at least until nine o'clock, it was the case that the princess was not asleep. Karttunen ( 1974) denies the durative character of negative sentences, and argues against the one until-theory. He claims that negation always takes wide scope over the until-phrase, so that (6a) is the only correct representation of the logical structure of the sentence. In this view, the different readings of (6) fall out from a lexical ambiguity in the predicate, which correlates with an ambiguity in the until-phrase. He argues that the verb sleep can have a stative reading under which it means 'be asleep' or an inchoative reading under which it gets the meaning 'fall asleep'. He claims furthermore that the negative polarity use of until is not durative but punctual: it is used to locate events in time. The claim that negative polarity until is not durative but punctual is supported by the combination of until with event predicates in negative sentences such as (Jc), but not in affirmative sentences like (3d). Karttunen ana lyzes punctual until as logically equivalent to before. Thus under the stative reading of the predicate and the regular durative interpretation of until, ( s ) means that it was not the case that the princess slept until nine o'clock (she woke up earlier). Under the inchoative reading of the predicate and the negative polarity, punctual reading of until, the princess would not begin to sleep before nine (that is, her falling asleep would occur at nine or later). There is more to the meaning of negative polarity until than its logical equivalence to before. Karttunen notes that the focus is not so much on the absence of an event in the period before a certain point in time (which is what (6b) conveys), but on the fact that the event only happens after a certain point in time. This use of until implies that the event does indeed take place, but that it occurred later than expected. According to Karttunen, (7a) commits the speaker to the truth of both (7b) and (7c):
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The intuition that nine o'clock is somehow late for the princess to wake up is further illustrated in (9) and (10) (Hom I 972 discusses analogous examples): (9) a. b. ( 1 0) a. b.
*The princess slept until nine at the earliest. The princess slept until nine at the latest. The princess didn't wake up until nine at the earliest. *The princess didn't wake up until nine at the latest.
(r r) a. The princess did not sleep until nine o'clock. b. The princess did not wake up until nine o'clock. It would be incorrect to claim that the princess woke up from nine o'clock onwards in ( 1 1 b). In order to account for non-durative sentences under nega tion, Tovena (1995) generalizes the composition approach, and claims that not . . . until is a complex operator expressing Allen's (I 984) START relation. Under this analysis, nine o'clock marks the start of the waking-up event in (I I b). Both proposals underline Karttunen's claim that not . . . until focusses on the location in time of the event, rather than its absence until then. The feeling of'lateness' is not explained, though. Declerck's (1995) proposal is the best-worked-out version of the lexical composition approach. It accounts for both the focus on the actualization of the event and the idea oflateness by treating not . . . until in
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Intuitively, (9) stretches the duration of the state as long as possible, whereas ( 10) focusses on the earliest possible moment the situation can hold. In order to capture this feeling of'lateness', Karttunen assumes that negative polarity until t pramatically presupposes that the event occurs before or at t. The time period beginning at t is then the very last cut of the time stretch during which we would expect the event e to occur, so it happens late. According to Karttunen, neither the intuition that the event is thought of as actually happening, nor the feeling oflateness are captured by the scope analysis. He takes this as additional evidence for his ambiguity approach: it will be part ofthe lexical meaning of the negative polarity item until. Mitrwoch (I 977) acknowledges that her scope analysis captures neither the inference that the event actually happens, nor the idea of 'lateness'. However, she argues that this is not crucial, because these meaning effects are implicatures. As such, they are part of the pragmatics of not . . . until, and do not motivate an analysis of negative polarity until as a separate lexical item. As far as the semantics is concerned, Mitrwoch claims that there is insufficient evidence in favor of the rwo untils-theory, and that it is enough to have j ust one, durative until. A third line of study treats negation as composing directly with the temporal connective. According to Hitzeman (I 99 I ), negation reverses the meaning of until in such a way that 'at all times up to t' gets to mean 'from t onwards'. Although such an analysis can account for examples like ( I I a), it does not work for cases like ( I I b):
Henriette de Swart
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English as a stereotyped unit meaning 'only'. One argument in favor of this approach is that not . . . until is lexicalized in other languages as one word, e.g. German erst, and Dutch pas. Although not mentioned by Declerck, we can add that it is not uncommon for exclusive focus particles to be realized as a discontinuous unit involving negation, e.g. French ne . . . que. Declerck's analysis is interesting, because it captures most of the semantic and pragmatic meaning aspects of not . . . until. According to this interpretation, the event actually occurs, because exclusive particles akin to only generally come with a presupposition which triggers this effect, and the event occurs late, because the alternatives are ordered on a scale.
The structure ofthe paper
The three treatments of not . . . until briefly presented here each have their own attractive features. The question arises which one best describes the semantics and pragmatics of the construction. Mittwoch's scope analysis has the advantage of defending the most conservative approach. Scope ambiguities play an important role in semantic theory, so there is nothing particularly strange about the interpretation of not . . . until. It is a drawback for boi:h the ambiguity thesis and the lexical composition approach that they have to postulate two untils. As a result, the properties of until in negative sentences have to be stipulated separately, and cannot be derived from its use in affirmative sentences. Thus, these analyses do not observe the principle of compositionality of meaning. However, Karttunen's ambiguity thesis and Declerck's lexical composition approach seem to be able to explain certain aspects of the meaning of not . . . until which are not addressed by the scope analysis. This concerns in particular the implicature that the event actually takes place, and the feeling of 'lateness'. It is hard to evaluate the different proposals at this point, mainly because none of the authors provide a formal analysis of until. The aim of this paper is to make the meaning and use of until and not . . . until precise by providing an explicit interpretation in an event-based temporal semantics. Part of the issue whether aspectual adverbials have a separate use as negative polarity items revolves around the question of the aspectual character of negative sentences. The one until theory makes crucial use of negation as an aspectual operator, whereas Karttunen and others deny that negative sentences are durative. In section 2, I discuss some of the general combinatorial criteria used to determine the aspectual character of sentences. It turns out that data from French provide sufficient evidence to conclude that negative sentences are durative. I argue furthermore that negative sentences are referential in the sense that they inttoduce a discourse referent which corresponds with the negative state of affairs described by the sentence as a whole. In section 3, I develop an analysis of regular durative until in event semantics.
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I .2
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2
N E G A T I O N A N D D U RAT I V I T Y 2.1
Combinatorial criteria
A number of linguistic tests have been developed to distinguish durative and non-durative sentences. For instance, durative sentences combine with Jor adverbials, whereas non-durative sentences combine with in -adverbials, and with the aspectual verb take: ( I 2) Jor-adverbials a. Susan loved Paul for many years. b. Andrew swam for three hours. c. #Eve drew a circle for three hours.4 d. #Mary reached the summit for two hours. ( 1 3) in -adverbials a. #Susan loved Paul in many years.5 b. #Andrew ran in three hours.
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In section 4, I extend the analysis to the semantics of negative sentences involving until, spelling out the scope analysis, the ambiguity thesis and the lexical composition approach in this framework. The conclusion is that for sentences which involve an explicit occurrence of negation, the three analyses are truth-conditionally equivalent. They all interpret not . . . until as defining exclusion on a temporal scale. Section s addresses the pragmatics of not . . . until. Given certain independently motivated pragmatic assumptions, I argue that even the scope analysis generates the implicature that the event actually arises. Karttunen's intuition that the event occurs 'late' turns out to be related to the interpretation of not . . . until as an expression of scalar exclusion in the temporal domain. All three approaches then generate the same pragmatic implicatures. Section 6 discusses a number of contexts which potentially allow us to discriminate between the three different treatments of not . . . until. The scope and polarity analyses develop different, but equivalent representations for sentences expressing exclusion on a temporal scale in German, Dutch, French, and Finnish. The lexicalist approach does not provide insight into the way the complex meaning is built up in different languages. Although Karttunen claims otherwise, the cross-linguistic comparison does not provide evidence in favor of the ambiguity thesis. However, examples of until which do not involve negation or durative contexts, but which occur in contexts which license negative polarity items cannot be explained under either a scope analysis, or a lexical composition approach. I conclude that this provides evidence in favor of a separate use of until as a negative polarity item, and that Karttunen's analysis is j ustified.
Henriette de Swart 227
c. Eve drew a circle in ten minutes. d. Mary reached the summit in three hours. ( I 4) take a. # It took Susan many years to love Paul. b. # It took Andrew three hours to run. c. It took Eve ten minutes to draw a circle. d. It took Mary three hours to reach the summit. If we limit ourselves to these combinatorial tests, we seem to be forced to the conclusion that negative sentences are both durative and non-durative, for they combine with for- and in -adverbials alike, as observed by Krifka ( I989):
The situation is further complicated by the fact that negative sentences do not combine with take, as shown in (I s c), which suggests that the criteria used are inconsistent in some sense. There are different ways in which one can try to solve this puzzle. One option is to say that the combinatorial criteria only apply to affirmative sentences and that for and in behave in different ways in negative sentences. This is the position adopted by Vlach ( I 993), who argues that the time adverbials in ( I s) double as negative polarity items. As such, they don't tell us anything about the aspectual character of negative sentences. This is essentially the ambiguity thesis extended to other time adverbials. A good argument in favor of the classification of some expression as a negative polarity item is to show that it is licensed not just by negation, but by certain non-negative expressions which typically license negative polarity items as well. Following this line of argumentation, Vlach ( I 993) refers to Mittwoch ( I 98 8) who points out that for- and in -adverbials also occur in sentences containing superlatives, and closely related expressions such as thefirst/last/only (c( Hoeksema I 986):
( I 6) a. This is the liveliest party I have been to for/in a long time. b. This is the first/only proper meal I have had for/in weeks. According to Vlach, any attempt to read these sentences with the ordinary durative interpretation of for runs into obvious problems. If we treat the aspectual adverbials in ( I 6) as negative polarity items, there is no reason not to do the same in (I s). Vlach concludes that we need not ascribe any aspectual effect to negation. One way to determine the aspecrual character of negative sentences without the interference of negative polarity is to carry out a cross-linguistic study of the combinatorial criteria. This is the approach adopted in de Swart (I99S)· One
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( I s) a. Jane did not drink (a glass oD wine for two days. b. Jane did not drink (a glass oD wine in two days. c. *It took Jane two days not to drink (a glass oD wine.
228
Meaning and Use of not . . . until
example of a language in which there is no interference between durative time adverbials and negative polarity is French. We observe that durative time adverbials introduced by pendant combine with negative sentences:
Negative sentences do not combine with non-durative en-adverbials: (I 8) en-adverbials a. #Michele a couru en trois heures. Michele has run in three hours. c. Michele a ecrit une lettre en une demi-heure. Michele has written a letter in half an hour. d. #Michele n'a pas ete au marche en trois mois. Michele has not been to the marketplace in three months. e. #Je n'ai pas vu Michele en trois mois. I haven't seen Michele in three months. Neither pendant- nor en-adverbials combine with superlatives or other contexts which typically trigger negative polarity items. Compare the sentences . in (19) and (2o) (from Fauconnier 1 98o): (I9) a. *C'est le premier/seul bon repas que j'aie eu en/pendant trois mois. This is the first/only good meal I have had in/for three months. b. *C'est le meilleur repas que j'aie eu en/pendant trois mois. This is the best meal I have had in/for three months. (2o) a. Ce cadeau est le plus beau qu'on m'ait jamais fait. This present is the most beautiful one has ever given me. b. C'est le seul homme politique qui soit du tout honnete. It's the only politician who is at all honest. On the basis of the French data, I conclude that negative sentences are durative. They only combine with non-durative adverbials in languages (such as English) in which these expressions also show up in contexts which license negative polarity items.
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( I 7) pendant -adverbials a. Michele a ete malheureuse pendant des annees. Michele has been unhappy for years. b. Michele a couru pendant trois heures. Michele has run for three hours. c. #Michele a ecrit une lettre pendant trois heures. Michele has written a letter for three hours. d. Pendant des annees , Michele n'aima pas le chocolat. For years Michele didn't like chocolate. e. Pendant trois semaines, Michele n'est pas rentree a la maison. For three weeks Michele didn't come home.
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Negative states ofaffairs
(2 1 ) a. John didn't know the answer to the problem. This lasted until the teacher did the solution on the board. b. John did not ask Mary to dance at the party. It made her angry. If Hwang and Asher are right that we need some (discourse) entity as the referent for the pronouns this and it, we seem to be committed to this position for both affirmative and negative sentences. However, (2 1 ) could still be taken to confirm Asher's view that the negation of an event refers to a fact. An interpretation in terms offacts is not appropriate for sentences like (22), though:
(22) What happened next was that the consulate didn't give us our visa. Assuming with Vendler ( 1 967), Horn ( 1 989: s s), and others that only events, and not facts, can 'happen', it looks like we have a negative event here, and not simply a fact. A third argument in favor of the referential character of negative sentences is provided by Stockwell, Schachter, & Partee ( 1 97 3), who point out that there are cases where the negation of an event may, loosely speaking, itself be an 'event'. They discuss cases like not paying taxes, not getting up early, not going to church , not eating dinner, etc., which involve the breaking of a habitual or expected pattern of activity. This type of eventuality can even be embedded under frequency adverbs:
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The combinatorial criteria distinguish between durative and non-durative sentences. Verkuyl ( 1 993) classifies negative sentences as states. In de Swart ( 1 995), I provide further evidence in favor of this position. One argument is that negative sentences are true at all instants of the interval for which the sentence holds, which is the defining property of states according to Dowty ( 1 979). One consequence of the position that negative sentences denote negative states of affairs is that I actually claim there is a discourse referent for the negative sentence as a whole. This discourse referent is a state, irrespective of the question whether the sentence embedded under the negation operator refers to a state or an event. In this, I differ from Kamp & Reyle ( 1 993) for instance, who claim that negation is a closing operator, and who interpret negative sentences as the absence of an event, rather than the state of something not happening. Given that this could be argued to be a more conservative approach, my position needs some further motivation. One argument in favor of the idea that negative sentences introduce their own discourse referent comes from the observation that negative sentences license discourse anaphora. The following examples are provided by Asher ( 1 993) and Hwang ( 1 992) respectively:
2 30
Meaning and Use of not . . . until
(23) a. He often hasn't paid taxes. b. He sometimes doesn't eat dinner. c. He doesn't eat dinner two nights a week.
3 UN TIL I N EVENT S E M A N T I C S 3.1
General notions ofevent semantics
I adopt a neo-Davidsonian analysis, and assume that all predicates come with an extra event argument. Tenseless clauses are interpreted as denoting sets of eventualities, that is, members of the domain of eventualities e. A verb which has all its argument places filled by either constants or variables provides an atomic eventuality description. Such eventualities are in general conceived of as minimal: the eventuality does not contain anything in addition to what is supported by the predicate-argument structure. The domain e of eventualities is partially ordered by a part-whole relation � and a precedence relation <,. There is a join operation q so that e has the structure of a complete join semilattice. It is well known in temporal semantics that eventualities come in aspectually different types. In the analysis of until, we need the contrast between durative eventualities (states and activities), and non-durative events. For the purposes of this paper, I do not need to establish an ontological distinction between states
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All these sentences allow a reading in which the frequency adverb has scope over negation, meaning that they describe the frequency of a negative situation. According to Stockwell, Schachter, & Partee, sentences like (23) are a counter example against Lakoff's claim that 'one cannot assert the frequency of an event that does not occur' (Lakoff I 965 : I 72). We can add that adverbs of quantifica tion do not quantify over facts, but over eventualities (c£ de Swart, I99I ). Clearly, the kind of examples in (2 I), (22), and (2 3) are only felicitous in contexts in which the denial that a certain event took place is informative enough to be stated. This requires something like an unfulfilled expectation or the breaking of a regular pattern. Horn ( I 989: 20 I) argues that this is a pragmatic matter: the asymmetry is not located in the relation between propositions (negative vs. affirmative), but in the relation between speech acts (denial vs. assertion). In this perspective, (2 I)-(2 3) show that we gain more insight in the temporal semantic properties of negative sentences when we adopt an analysis in terms of negative state of affairs.6 The conclusion that negative sentences are durative removes one of Karttunen's objections against the scope analysis. In order to compare the different analyses of not . . . until in more detail, we need to spell out the contribution of until in some version of temporal semantics.
Henriette de Swart 2 3 1
(24) The princess slept. a. A.s [Sleep(princess,s) 1\ 3t AT(e, t)] b. 3s3t [Sleep(princess,s) 1\ AT(e, t) 1\ t < n ] The untensed sentence introduces a set of states (24a). The tense operator leads to the representation in (24b), which claims that one such state is located at a time preceding the utterance time.
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and activities, so I will keep them together in the class of durative situations, which I refer to as states. Among the set c of eventualities, there is a subset E of events and a subset S of states, which form complete join semilattices of their own. Every eventuality is either a state or an event, that is c - E u S. An important difference between the two classes of eventualities is that states have divisive reference, that is, parts of the state satisfy the same description as the state as a whole. Events on the other hand have quantized reference: parts of the event do not qualify as the same event. Also, states have cumulative reference, but events do not. That is, any two eventualities can combine to form a third eventuality (Krifka 1 989; Lasersohn 1 990), but the join of two events will not be of the same event type. Whether a sentence introduces a state or an event variable is partly determined by the lexicon (to be rich is a state, to come in is an event), and partly by the semantic character of the arguments of the predicate (to write a letter is an event, to write letters is an activity). In this paper, I will not be concerned with the exact procedure by means of which the aspectual character of atomic predicates is determined (but see Krifka 1 989 or Verkuyl 1993 for compositional analyses). I will simply take it for granted that there is such a procedure, which yields either a state or an event variable for every (untensed) sentence. In order to locate events in time, we need a domain T of times (points or intervals on the time axis), and a precedence relation <, which leads to a total order ofT. A function AT from c to T maps eventualities on to their location on the time axis, which Krifka ( 1 989) calls the 'run time' of the eventuality. For an eventuality e to hold at a time t will be written as AT(e, t). Tense operators induce existential closure over the eventuality variable. The past tense introduces the condition t < n which leads to the interpretation that the (minimal) event holds at a time t which precedes the speech time n ('now'). The present tense introduces the condition n s; t. I interpret the future tense as non past rather than strictly future, which leads to the condition n 5 t. All further complexities which arise in the interpretation of tense operators (or aspectual operators such as the Progressive) will be ignored in this paper. Consider (24) under the regular durative interpretation of the predicate:
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Meaning and Use of not . . . until 3 .2
The interpretation of until
"
o
For y: A.s[P(s) 1\ 3t AT(s, t)J and o: At' Q (t'): iiuntil( y , o)ii A5 3t3t' 3t'"[P(s) 1\ AT(s, t '") 1\ Q(t') 1\ t � t'" 1\ \lt"[[ts t" < t'] - 3s' [s' b s 1\ P(s') 1\ AT(s', t ")]]] �
This roughly corresponds with the interpretation of the temporal operator U as defined by Kamp (1968), but reformulated in an event-based semantics. Following this definition, a sentence like (25) is interpreted as in (z sa): (zs) The princess slept until nine o'clock. a. 3s3t3t' 3t'"[Sleep(pr, s) 1\ AT(s, t"') 1\ t'" < n 1\ Nine(t') 1\ t� t'" 1\ \lt"[[tS ( s t'] - 3s' [s' b s 1\ Sleep(princess,s') 1\ AT(s', t")]]] (zsa) spells out the intuition that there is a situation of the princess being asleep which holds at some time t'" in the past which includes a time t. Furthermore, there is a time t' of nine o'clock, and at every time t " preceding t' and going all the way back to t, it is the case that the princess slept? Universal quantification over times preceding the time of the adverbial guarantees a durative inter pretation of the main clause. Remember that states and activities, but not events have divisive reference. Thus it is possible for states and activities to have a part of the situation which satisfies the same description to hold at all times preceding the time of the time adverbial. For events this is impossible. (Minimal) events only hold at the interval as a whole, and part of the event does not satisfy the same event description. This correctly rules out such ungram matical sentences as (26):
(26) a. *Susan wrote a letter until midnight. b. *The princess woke up until nine o'clock. (zsa) shows that until introduces existential quantification over the time t' of nine o'clock. As far as clock adverbials are concerned this seems an
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Further constraints on the location time t can be provided by locating time adverbials. Just like verbs are treated as predicates of eventualities, temporal nouns such as nine o'clock, Sunday are treated as predicates of times, that is, points or intervals on the time axis. Such clock expressions are part of a cyclic system, and identify times which are separated from each other by a fixed distance on the time axis. Prepositions such as on , before , after, until establish a relation between the event denoted by the main clause and the time denoted by the temporal noun. Until introduces a range of values on the time scale. These are the times t " which precede the time t' referred to by the clock expression o with description Q. In affirmative sentences, (part o� the situation s with description P provided by the (durative) main clause y is claimed to hold at all these times t . The semantics of until is formally defined as follows:
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uncontroversial assumption: there will always be a time ofnine o'clock. As soon as we study temporal clauses introduced by until, the claim of existence does not always hold, which will lead to a modification of the analysis. This issue will be taken up in section 5.2 below. Note that the use of a clock expression like nine o'clock normally selects the time of nine o'clock nearest to the speech time or reference time. A condition which guarantees that the nearest time is selected can easily be added, but for the sake of transparency of the definition I will not make this requirement explicit. Of course the princess did not sleep at all times going back to the beginning of the earth. In (2sa) there is a beginning point t for the interval we take into consideration, which Kamp & Reyle ( 1 993: 634) suggest could have been made explicit with a from-phrase as in (27): In (25), the beginning point of the interval is not explicitly defined. It is contextually given, and I assume that there are appropriate implicit restrictions on the domain of quantification which handle this. In the case of the future tense, t is often (but not always) identified with the speech time. The only restriction I impose on t is that t is chosen somewhere in the run time of the situation of the princess being asleep, so that (part of) the state occurs at the beginning point of the interval we are int�rested in. Although t and t' are the beginning point and the endpoint of the interval taken into consideration, I do not make the claim that the state s of the princess being asleep did not start earlier or continue later. If this is inferred from the sentence, it is an implicature (Grice 1975), not an assertion. The fact that the speaker explicitly defines the boundary of the interval suggests that she knows until which time the state lasted. If she knew that it lasted longer, by the principle of cooperative conver sation and the maxim of quantity, she should have said so. Stating that the princess slept until nine o'clock then implicates that she did not sleep any longer.8 4 T HE S E M A N T I C S O F NO T . . . UNTIL The definition of durative until provides the starting point for a more detailed discussion of the meaning of not . . . until. I will first spell out how a scope analysis can be formulated in the event-based framework I have adopted, and then do the same for the ambiguity thesis and the lexical composition approach. 4· I As pointed out in section
The scope analysis
I , Smith and Mittwoch assume that the ambiguity of a sentence like (28) is due to the fact that negation can take either wide (28a) or narrow (28b) scope with respect to until.
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(27) The princess slept from midnight until nine o'clock.
234
Meaning and Use of not . . . until
(28) The princess did not sleep until nine o'clock. a. --. (until nine o'clock (the princess slept)) b. (until nine o'clock (--. (the princess slept))) The interpretation of the wide scope reading of negation is worked out in (29): (29) The princess did not sleep until nine o'clock a. It is not the case that the princess slept until nine o'clock. (She woke up earlier, e.g. at seven.) b. -. 3s3t3t'3t'"[Sleep(pr,s) 1\ AT(s, t"') 1\ Nine(t') 1\ t � t'" 1\ \lt'' [[t S t" < t' ] 3s' [s' b; s 1\ Sleep(princess,s') 1\ AT(s', t ")]]] c. 3s3t3t'3t'" [Sleep(pr,s) 1\ AT(s, t'") 1\ Nine(t') 1\ t � t'" 1\ --. \ft''[[tS t" < t' ] 3s' [s' b; s 1\ Sleep(princess,s') 1\ AT(s', t' ' )]]] -+
(29b) is the negation of(25a).9 As usual, the negation of a conjunction comes out true as soon as one of the conjuncts is false. In principle, then, there is a series of possible situations which can make (29b) true. One of them is to assume that there is a (nearest) rime of nine o'clock and that the princess slept at some point in time in the past, but to deny that the situation lasted until nine o'clock. This possibility is spelled out in (29c). Note that (29b) and (29c) are not equivalent. Strictly speaking, there is not even an entailment relation between them. (29c) comes out true and (29b) false in case there is a situation of the princess sleeping which didn't last from t until nine o'clock, but there is at least one other situa tion of the princess sleeping which did last from t until nine o'clock. This can only be true if a situation of the princess being asleep can be included in another situation of the princess sleeping without being considered part of that situa tion. The question of identity of events, and the distinction between two eventualities sharing the same descriptive content, and overlapping partly or completely in their location rime raises important problems in event semantics. Although I will not commit myself to the claim that there never are two co temporal but different eventualities which satisfy the same description, I will assume that this is normally not the case. Modulo this assumption about 'n0rmal' event structures, (29c) entails (29b). Two clearcut contexts in which (29b) comes out true and (29c) comes out false are situations in which there is no (nearest) time of nine o'clock or there is no state of the princess being asleep at some point in rime in the past which includes t. Unless the sentence is used to express a meta-linguistic negation in the sense of Hom ( 1 989), these cases are not relevant contexts with respect to which we want to evaluate our sentence, though. As we observed above, it is natural to assume that there will always be a (nearest) rime of nine o'clock, independently ofwhat happens at that rime. Independently motivated assump tions about the characterization of the rime axis then rule out the possibility of falsifying that conjunct, and it is defacto outside the scope of negation. If the
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speaker wanted to deny that a situation o fthe princess sleeping ever occurred, it would make much more sense to use a sentence like (30) than (29): (30) The princess didn't (ever) sleep.
(3 1 ) 'V e[MAX(e) - 3t [ e - supJA.e'3t'(AT( e', t') 1\ t' <;; t))]] Here sup, is the supremum in the join semilattice of eventualities e, which gives us the sum of all eventualities e' occurring at some time t' included in t. Negative eventualities refer to maximal eventualities which do not satisfy the eventuality description at a given time t. Following Krifka again, we define event predicate negation as in (32): (32) A.PA.s [MAX(s) 1\ -.3 e[P( e) 1\ e <;; s]] Negation is thus a modifier which operates on an eventuality description P and yields the maximal state s such that no eventuality e of type P is contained in s. For the reading of (33) with narrow scope for negation, this view leads to the paraphrase in (3 Ja) and the representation in (3 3b): (33) The princess did not sleep until nine o'clock a. A situation in which the princess did not sleep lasted until nine o'clock. b. 3s3 t3t'3t"' [MAX(s) 1\ (-.Sleep)(princess,s' ) 1\ AT(s, t' ") 1\ t <;; t'" 1\ Nine(t') 1\ \ft'' [ [t � t'' < t'] ..... 3s'[s' 6 s 1\ (-. Sleep)(princess,s') 1\ AT(s', t' )] ]] '
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The Gricean Maxim of Manner saying 'be brier requires the speaker to choose the less complex one out of two, equally informative expressions. If the speaker adds a time adverbial in (29), and wants the time adverbial under the scope of negation, this should be relevant. Because of the existence of a straightforward alternative (namely (3o)), it is most relevant when the situation denoted by the main clause occurs, but does not satisfy the relation denoted by the temporal connective. This leads to the interpretation in (29c), which correctly reflects the intuition that the princess woke up earlier than at nine. Smith and Mittwoch's claim that the other reading of(29) corresponds with a narrow scope interpretation for negation requires us first to interpret event negation in our framework. In section 2.2 above, I defended the view that negative sentences introduce their own discourse referent, and describe a state which corresponds with a negative state of affairs. We can establish a natural relation between a negative state of affairs and the state or event it is the negation of by following Krifka's ( 1 989) proposal to interpret negative eventualities as the 'fusion' of all eventualities at a given time t which are not of the type of 'the princess being asleep'. In a lattice-theoretical framework, maximal eventualities are interpreted as the sum of all events at some point in time. My definition of maximal eventuality in (3 r ) is based on Krifka's:
236 Meaning and Use of not .
. . until
c. 3 t3t'3t"'(--.3s3t""(Sleep(princess,s) 1\ AT(s, ( ' ") 1\ ( ' " � t'"] 1\ t � t"' A Nine(t') A \ft''[( t s t'' < t'] ..... --. 3s' (Sleep(princess,s') 1\ AT(s', t")]] ] d. 3 t3 t [Nine( t') 1\ \ft"[[ts t" < t') --.3s (Sleep(princess,s) 1\ AT(s , t")]]] '
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(3 3b) claims that at some point in time in the past, it was the case that the princess did not sleep, and for all times until nine o'clock, it was the case that there was a situation of the princess not sleeping holding at that time. Negation now just affects the main clause. In this interpretation, we crucially rely on the negative sentence denoting a durative situation. In Mitrwoch's view, it is the durative nature of negative sentences which allows them to combine with until. In the event semantics adopted here, Mittwoch's claim is reflected in the assumption that there is a state of affairs corresponding with the negation of the princess being asleep. The discourse referent introduced outside the scope of negation is a state variable, whether the predicate embedded under the negation operator is an event predicate or a state predicate. Once we have the state of affairs corresponding with the princess not being asleep, we can use the regular durative interpretation of until which requires a part of that situation to hold at all times up until nine o'clock as in (3 3b). Following Krifka's interpretation of event negation, (3 3b) is equivalent to (33c): the period of time during which the situation of the princess not being asleep lasts includes no situation of the princess being asleep. (33c) can be further reduced to (3 3 d). It is easy to see that (3 3c) entails (3 3d). But (3 3d) entails (3 3c) as well: if there is no situation of the princess being asleep berween t and t' (as claimed by (33d)), there is an interval t'" which includes the period of time from t to t' at which no situation of the princess being asleep holds (- c). This in turn allows us to define the (maximal) negative state of affairs of the princess not being asleep as holding at t'" (- b). The formulas in (33b), (c) and (d) are thus equivalent. As far as the scope analysis is concerned, both readings of the sentence 'The princess did not sleep until nine o'clock' involve a durative time adverbial. Even so, the formulas in (29c) and (3 3d) are not equivalent. The first one has negation taking wide scope over the universal quantifier associated with until, the second one has negation taking narrow scope with respect to the universal quantifier. So we end up with rwo logically distinct readings, and the sentence is truly ambiguous. Sentences which involve an event predicate are not ambiguous. Unless it triggers the phenomenon of implied durarivity discussed in section 6. 3 below, the event predicate is incompatible with the durative rime adverbial, so a wide scope interpretation of negation over the until-phrase is excluded. The interpretation of negation as an aspectual operator allows a narow scope interpretation of negation, though. This leads to the interpretation of (34) spelled out in (34a-d):
Henriette de Swart 2 37
(34) The princess did not wake up until nine o'clock. a. A situation in which the princess did not wake up lasted until nine o'clock. b. 3s3 t3 t'3t'"[MAX(s) 1\ (_,Wake-up)(princess,s) 1\ AT(s, t'") 1\ t � t'" 1\ Nine(t') 1\ Vt"[[t S t" < t') -+ 3s' [s' b; s 1\ (-. Wake-up)(princess,s') 1\ AT(s', t'')]]] c. 3t3t'3t"'[-. 3e3t""[Wake-up(princess,e) 1\ AT(e, t''") 1\ t"" � t'") 1\ t � t'" 1\ Nine(t') 1\ Vt" [[t s t'' < t') 3e' [Wake-up(princess,e') 1\ AT(e' , t' ')])] d. 3t3t'(Nine(t') 1\ Vt"[[t s t'' < t') _, 3e [Wake-up(princess,e) 1\ AT(e, t")]]] __,
4.2
The ambiguity thesis
Under the ambiguity thesis, the correct semantic representation of (3 s) is as in (3 sa), with wide scope of negation over the until-phrase: (3 s) The princess did not sleep until nine o'clock. a. -. (until nine o'clock (the princess slept)) The ambiguity of (35) is due to an ambiguity in the predicate sleep and in the connective until. Given that Karttunen recognizes the negation of durative until as one of the readings of the sentence, we can work out this interpretation of (35) exactly as in (29) above. I take it that Karttunen and Srnith/Mittwoch agree on the interpretation of this reading of (3 s). According to Karttunen, the other interpretation of (3 s) arises from a negative polarity, punctual until. He claims that in this use, until is logically equivalent to before. I will interpret before as involving existential quantification over times t preceding the time t' denoted by the time adverbial. The semantics of before is formally defined as follows:10 •
For y. A.e[P(e) 1\ 3t AT(e, t)) and b: U Q(t'): libefore( y, b )ll .A.e3t3t'3t" [P(e) 1\ AT(e, t'') 1\ Q(t') 1\ t s t" < t') =
In most uses of before, the event cannot happen at just any time before the time specified by the adverbial, but it has to happen in the vicinity of that time. This is captured by introducing a contextually given interval of time between t and t' within which the event is expected to take place. For a sentence like (36), this definition of before leads to the interpretation in (36a): (36) Jane left before nine o'clock. a. 3e3t3t'3t" [Leave(j, e) 1\ AT(e, t'') 1\ Nine(t') 1\ t S t'' < t')
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This interpretation of (34) excludes an event of the princess waking up in the time interval from t to t' .
2 38
Meaning and Use of not . . . until
Karttunen's claim that sentences involving the negative polarity use of until are interpreted as NOT(e BEFORE t) in combination with an event reading of the predicate requires us to interpret sleep in (37a) not as the state of being asleep, but as the event of falling asleep. This interpretation leads to the paraphrase of (37) in (37a), and the interpretation in (37b), where the predicate introduces an event variable e, rather than a state variable s:
(37b) gives negation wide scope over the sentence as a whole, but unless the sentence is used to express a meta-linguistic negation, the pragmatic scope of negation will be narrower than that. If we assume that there is always a nearest time of nine o'clock, we can move this condition outside the scope of negation (37c). The Maxim of Manner favors the shorter over the longer expression, so it only makes sense to utter the sentence with a wide scope reading of negation over the time adverbial if the main clause event itself is presupposed to happen. This interpretation is spelled out in (37d), which best captures Karttunen's intuition about negative polarity until: it claims that the princess fell asleep, but that this did not happen before nine o'clock. It must thus have happened at nine or some time after. Although both the durative and the polarity interpretations of until in (29) and (37) involve a wide scope interpretation for negation as desired, the formulas in (29c) and (37d) are clearly not equivalent. The former involves the negation of a universal quantifier over times preceding nine o'clock, and the latter the negation of an existential quantifier over times preceding nine o'clock. The formulas in (29) and (37) thus correctly reflect the ambiguity of the sentence. From these interpretations it follows that sentences involving non stative predicates are not ambiguous. After all, the kind of interpretation in (29) crucially relies on the interpretation of until as a durative time adverbial. Given that event predicates do not combine with durative time adverbials in general, they will only give rise to the kind of interpretation sketched in (37). An example is worked out in (38): (38) The princess did not wake up until nine o'clock. a. The princess did not wake up before nine o'clock. b. 3t ....., 3e3t'3t"[Wake-up(princess,e) 1\ AT(e, t") 1\ Nine(t') 1\ t::; t" < t']
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(37) The princess did not sleep until nine o'clock. a. The princess did not fall asleep before nine o'clock. b. 3t ....., 3e3t'3t" [Fall-asleep(princess,e) 1\ AT(e, t") 1\ Nine(t') 1\ t � t" < t') c. 3t3t'[Nine(t') 1\ ....., 3e3t" [Fall-asleep(princess,e) 1\ AT(e, t") 1\ t � t" < t')] d. 3e'3t3t'3t'"[Nine(t') 1\ Fall-asleep(princess,e') 1\ AT(e', t'") 1\ ....., 3e3t" [Fall-asleep(princess,e) 1\ AT(e, t") 1\ t � t'' < t'])
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c. 3t3t'(Nine(t') 1\ -. 3e3t"(Wake-up(princess,e) 1\ AT(e, t'') 1\ t 5 t" < t']) d. 3e'3t3t'3t'" (Nine(t') 1\ Wake-up(princess,e') 1\ AT(e', t'") 1\ -.3e3t" (Wake-up(princess,e) 1\ AT(e, t'') 1\ t 5 t'' < t'])
o
General relation between 'start to be AD]' and 'be AD]': \fe\ft [(Start-to-be-ADJ(e) 1\ AT(e, t)] ..... 3s3t'(t :::X: t' 1\ Be-ADJ(s) 1\ AT(s, t')]]
The symbol :X: is introduced by Kamp & Reyle ( 1 993) to describe an 'abut' relation. It captures the intuition that the state of being ADJ holds at a time t' adjacent to the time t at which the event of starting to be ADJ occurs. A related claim is that, for all states which do have a beginning point, the (maximal) state of being ADJ at some time has a starting-to-be-AD] event at its initial border. This is formulated as the following inference: o
General relatio� between 'be ADJ and 'start to be AD]': \fs\f t' ((Be-ADJ(s) 1\ MAX(s) 1\ AT(s, t')] ..... 3e3t(Start-to-be-ADJ(e) 1\ AT(e, t) 1\ t ::X: t']]
This last inference pattern is sufficient to guarantee that (3 3d) entails (37c): (39) 3t3t' (Nine(t') 1\ \ft''((t 5 t'' < t'] ..... -. 3s (Sleep(princess,s) 1\ AT(s, t'')]]] ..... 3t3t'(Nine(t') 1\ -. 3e3t" (Fall-asleep(princess,e) 1\ AT(e, t'') 1\ t S t'' < t'])
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The negative polarity interpretation of until claims that there is an event of the princess waking up, but it did not occur before nine o'clock (38d). The question is now how the two interpretations given in (3 3) and (37), and (34) and (38) are related. It is easy to see that (34d) and (38c) are equivalent, because there is no difference in truth conditions between the wide scope of a universal quantifier over negation, and the narrow scope of an existential quantifier with respect to negation. The relation between stative sentences involving not . . . until in the two theories is a bit harder to establish. Karttunen and Srnith!Mittwoch agree on the first interpretation of 'The princess did not sleep until nine o'clock', which presupposes that the situation occurred, and asserts that it did not last until nine o'clock (29). There are two problems in comparing the other reading of the sentence. The first one is that Karttunen denies that negative sentences denote states, but we can solve that by using (3 3c) or (d) rather than (3 3b) for comparison. The second problem is that Mittwoch does not interpret sleep as an event predicate. So in order to establish a comparison, we need to determine the relation between falling asleep and being asleep. If we interpret falling asleep as starting to be asleep, we can argue that every event of falling asleep is immediately followed by a state of being asleep. This inference is an instantiation of the following pattern:
240
Meaning and Use of not . . . until
(39) shows that the narrow scope interpretation of negation entails the negative polarity interpretation. The implication in the other direction is not logically valid. The crucial counterexample is given by a situation in which there is no event of the princess falling asleep in the interval from t to t ', but it is nevertheless false that the princess is not asleep, because the princess fell asleep before t. She cannot fall asleep again in the period from t to t' if she is already asleep at t and continues to asleep until at least t' . However, this is intuitively not a relevant context with respect to which we want to compare the two analyses. I will make the pragmatic assumption that the statement that no event of the princess fell asleep during an interval is only relevant in a context in which the princess is not already asleep. Modulo this assumption, (37c) implies (3 3d), so the scope analysis and the ambiguity thesis are equivalent.
The lexical composition approach
Declerck ( 1 995) argues that not . . . until is a sterotyped unit which has the meaning of 'only', and is lexicalized in other languages by means of a simple lexical item. Karttunen ( 1 974) points out that a sentence like (4oa) translates with the positive polarity item erst in German (4ob). The Dutch particle pas is similar in use (4oc): (4o) a. The princess didn't wake up until nine o'clock. b. Die Prinzessin wachte erst urn neun Uhr au£ c. De prinses werd pas om negen uur wakker. Konig ( 1 99 1 : 3 8 and further) argues that erst is an exclusive focus particle akin to nur, which is the most straightforward translation of only. Both erst and nur imply that the contextually given alternatives (the C-set in Rooth's 1 992 tenninology) do not satisfy the open sentence in their scope. The main difference is that nur selects its alternatives from an unordered set, while erst is sensitive to the scale on which the alternatives are ordered. Konig illustrates the contrast between nur and erst with the minimal pair in (41 ): (41) a. Ich fahre nur am Donnerstag nach Miinchen. I only go to Munich on Thursday. b. Ich fahre erst am Donnerstag nach Miinchen. I do not go to Munich until Thursday.
Nur in (4 1 a) excludes any days before or after the day mentioned, if these days happen to be under consideration in the context. Erst in (41 b) only excludes days preceding the one denoted by the focus constituent, for it selects alternative values that are lower on the scale than the focus value. As a con sequence, (4 1 b) cannot be used if the speaker wants explicitly to exclude the Fri-
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4·3
Henriette de Swart
24 1
day or Saturday of a certain week. Within the event semantics developed in this paper, we can represent (4 1a) and (b) as in (42) and (43) respectively:
Both (42) and (43) appeal to a contextually determined set C of possible days at which I could have gone to Munich. This set needs to include at least one contextually relevant alternative time in addition to Thursday. For nur, C is just an unordered set. In (42), we can assume that C contains the days of the week. For a scalar particle like erst, the set of contextually relevant alternatives is ordered on a scale, which I interpret as a partially ordered set. Such a set of alternatives will be written as Cpo· In (43) the relevant order is provided by the time axis, so the partial order on the set of days is just temporal precedence. Erst excludes all values which are lower on the scale than Thursday (43a). In other words, no event of going to Munich occurs on any day of the week earlier than Thursday (43b). Furthermore, exclusive particles are usually taken to be presuppositional. If the fact that I went to Munich is assumed to happen, as in (43c), we can easily explain the implicature that it will happen on Thursday or shortly after from the exclusive character of erst.11 Unlike (42), (43) does not exclude the possibility that I also go to Munich on Saturday. Because Saturday is not lower on the scale (= earlier in time) than Thursday, and it is not part of the range of values that are explicitly excluded, my going to Munich on Saturday is not incompatible with the truth of (43). Typically, erst identifies values rather high on the scale, because this creates a pragmatically relevant set of alternatives. Thus (43) could be felicitously uttered on a Sunday, but not really on Wednesday night, because in the latter context there is no relevant alternative earlier than Thursday. It is a result of the scalar nature of the particle that (43), but not (42) gives the hearer the feeling that Thursday is rather late for a visit to Munich. In order to establish a comparison between the lexical composition approach and the two analyses developed above, we can spell out the inter pretation (44a) gets under the view that not . . . until is equivalent to erst in (44b) as in (44c). The identification of the scale with the time axis leads to the interpretation in (44d):
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(42) Ich fahre nur am Donnerstag nach Miinchen. a. 3t'(Thursday(t') 1\ \fe\ft'lt"[[t" E C A Go-to-Munich(I,e) 1\ AT(e, t) 1\ t � t"] - t" = t']] (43) Ich fahre erst am Donnerstag nach Miinchen. a. 3t' [Thursday(t') 1\ \fe'lt'lt" [[t" E cpo 1\ Go-to-Munich(I,e) 1\ AT(e, t) A t � t''] .... t' � t"]] b. 3t'3t'" [Thursday(t') 1\ VeVtVt"[[Go-to-Munich(I,e) 1\ AT(e, t) 1\ t � t''] - t'" s t' s t'']] c. 3e'3t'3t"'3t''"[Thursday(t') 1\ Go-to-Munich(I,e') 1\ AT(e', t"") 1\ VeVtVt" [[Go-to-Munich(I,e) 1\ AT(e, t) 1\ t � t''] .... t'" S t' S t"]]
242
Meaning and Use of not . . . until
(44) a. The princess didn't wake up until nine o'clock. b. Die Prinzessin wachee erst urn neun Uhr au£ c. 3t' [Nine(t') 1\ \fe\ft\ft'' [[t" E cpo 1\ Wake-up(princess,e) 1\ AT(e, t) 1\ t � t"]] t' � t'']] d. 3t'3t'" [Nine(t') 1\ \fe'v't'v't"[[Wake-up(princess,e) 1\ AT(e, t) 1\ t � t' ') t"' s t' s t'']) -+
-+
S· THE P R A G M AT I C S O F N O T . . . UNTIL s.I
Actualization ifthe event
Karttunen ( 1 974) points out that a sentence like (45) strongly suggests that the event of waking up actually occurs: (4S) The princess did not wake up until nine o'clock. Kartrunen accounts for this observation by assuming that negative polarity until comes with the pragmatic presupposition that the event occurs before t or at t. The negation excludes the possibility that the event occurs before t, so this induces the feeling that the princess wakes up at nine in (45). Declerck ( 1 995 ) explains Karttunen's observation as the result of the exclusive character of not . . . until in his analysis. Exclusive particles akin to only typically come with the presupposition that the expression modified by only satisfies the requirement. Thus (45) presupposes that the princess woke up at or shortly after nine, and asserts that no event of waking up occurs before that time. Both Karttunen and Declerck build the feeling of actualization into the lexical meaning of not . . . until. Mittwoch (1977) dismisses Karttunen's observations as rather irrelevant. Of course, under a scope analysis one cannot build a presupposition of
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Remember that the scope analysis claims that the situation of the princess not waking up lasts until nine. The negative polarity analysis claims that there is no situarion of the princess waking up before nine. The interpretation of not . . . until as an exclusive scalar particle locates the first possible situation of the princess waking up at nine or later. The formulas in (34d), (3 8c), and (44d) are different but logically equivalent, so the three different approaches yield the same truth conditions. The results for stative sentences are similar. The first conclusion of this paper is then that, if one accepts the way the three approaches are spelled out in the event semantics developed here, there are no semantic differences between the scope analysis, the ambiguity thesis, and the lexical composition approach: they all interpret not . . . until as expressing exclusion of a range of values on the time axis. If there are differences between the three approaches, then they must reside in the way they describe the pragmatics of this construction.
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actualization of the event into the semantics, because until gets the same semantics in affirmative and negative sentences. This means that the feeling that the event actually occurs can only be an effect of the pragmatics of the construction. Mittwoch (1 977) does not attempt a serious discussion of the pragmatics of n ot . . . until. This does not mean that the scope analysis has nothing to say about this problem. Under the scope analysis, a sentence like (46) can only be interpreted with narrow scope for negation as paraphrased in (46a). This leads to the interpretation in (46b) (- 34b):
The Gricean principle of cooperative discourse requires the speaker to be maximally informative. If the speaker asserts that the situation of the princess not waking up lasts until nine o'clock, this generates the implicature that the situation did not last beyond nine o'clock. Now, the normal way in which a situation of the princess not waking up ends is for the princess to wake up. This is an instantiation of a general relation between a state of affairs defined as the negation of an event and the event it is the negation of •
For all predicates P and all arguments x 1 Xn and event variables e such that P(x1 xn, e) describes an event, it is that case that: lfx1 xnlfslftlft'lft''[[(-.P)(x1 xn, s) 1\ MAX(s) 1\ AT(s, t) 1\ t' � t/\ t' < t'' 1\ -.3s' [s' b. s 1\ (-.P)(x1 xn, s' ) 1\ AT(s , t'')]] - 3e3t'" [P(x1 xn, e) 1\ AT(e, t'") 1\ t' < t'"� t'']] •
•
.
•
•
•
•
•
•
•
•
•
•
•
•
'
•
•
•
Using the general observation that the negative state of affairs ends with the event happening, and the implicature of until that the situation does not last beyond the time it is asserted of, I claim that, in the narrow scope interpretation of negation, (46) implicates that the princess woke up at or shortly after nine o'clock. According to Declerck ( 1 995: 69) such a pragmatic inference is not strong enough to account for the feeling that the event actually occurs. His main argument is that a conversational implicature cannot explain the difference between affirmative and negative sentences involving until. Consider (47) and (48): (47) a. b. (48) a. b.
Nancy remained a spinster until 1978. Nancy didn't get married until 1978. Nancy remained a spinster until she died. Nancy didn't get married until she died.
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(46) The princess did not wake up until nine o'clock. a. A situation in which the princess did not wake up lasted until nine o'clock. b. 3s3t3t'3t'"[MAX(s) 1\ (-.Wake-up)(princess,s) 1\ AT(s, t'") 1\ t � t'" 1\ Nine(t') 1\ lft''[[t s t'' < t'] 3s' [s ' b. s 1\ (-.Wake-up)(princess,s') 1\ AT(s', t")JJJ
244
Meaning and Use of not
.
.
.
until
{49) a. It will simply delay the debate until the qualifications are closed next spnng.
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Both {47a) and {47b) suggest that Nancy got married in 1 978. According to Declerck, the implicature in the first sentence is weaker than in the second one, though. He illustrates this with the pair of sentences in (48). (48a) does not suggest that Nancy got married. (48b), on the other hand, still has the sense of acrualization, and it is semantically anomalous because of this. Declerck concludes that the scope analysis does not offer a satisfactory explanation of the implicature of actualization. I do not think this conclusion follows from the data in (47) and {48). Note that the implicature we expect on the basis of our interpretation of regular durative until is that the situation ends at or shortly after the time given by the time adverbial. Which way the situation ends is of course dependent on the context. For (47a), the end of the situation of Nancy remaining a spinster is most naturally induced by marriage. However, in (48a), the situation ends with her death. After Nancy dies, she is no longer a spinster, because this concept simply does not apply to dead people. (47b) and (48b) are different. We just observed that the end of a state of affairs consisting of the negation of an event predicate is the occurrence of the event in question. In (47b) this gives rise to the implicature that Nancy did indeed get married. The siruation of not getting married does not end at Nancy's death in (48b): after she dies, she is still not getting married. The implicature that th� event actually occurs is infelicitous in this context, and therefore the sentence is pragmatically anomalous. However, Declerck's statement that the implicature is stronger than what can be calculated on the basis of the conversational principles has some intuitive appeal. One way to preserve the scope analysis, but make the implicature stronger, is to assume that the inference has been conventionalized and is short-circuited in the sense of Horn ( 1989). It is well known from the study of indirect requests that a given pragmatic inferencing mechanism may apply more directly to one expression than to another. For instance, 'Can you pass me the salt?' is conventionally used to request the salt, but 'Are you able to pass me the salt?' is not. As pointed out by Morgan (1978), the conventional usage of such indirect requests does not make it necessary to treat them as idioms. Along th�se lines, it is straightforward to assume that in the case of not . . . until, the implicature that the event actually happens is short-circuited, rather than calculated for every instance. The degree to which the implicature is conventionalized depends on the relation between the main and the subordinate clause. Sometimes this relation is purely temporal (49a), but in many cases it is causal in nature. Bree (198 5) observes that in general the until clause can be the cause of the ending of the main clause situation (49b), the result of the activity described by the main clause (49c) or the goal for which the main clause activity is carried out (49d):
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b. This cooling . . . just delays the natural softening of the fruit until a grovelike temperature is restored. c. And from that the stock moved right on up until it was trading Thursday morning at around 22 a share. d. Extend your feet forward and backward until you are in a deep leg split.
5 .2
More on (non)-actualization
Some interesting further questions concerning the interpretation of until arise when we take a closer look at (full) temporal clauses, rather than time adverbials. As observed above, it makes sense to introduce existential quantifi cation over the time denoted by the time adverbial in (so) as in (soa), because we can safely assume that such a time exists: (so) The princess slept until nine o'clock. a. 3s3t3t'3t'" [Sleep(princess,s) /1. AT(s, t'") /1. Nine( t') /1. t � t'" /1. Vt''[[t:'S t'' < t'] -+ 3s'[s' 6 s /1. Sleep(princess,s' ) /1. AT(s', t'')l]] We can extend this analysis to temporal clauses, and build in existential quantification over the event denoted by the until-clause. For examples like (s I ) this would be an uncontroversial assumption: (s I ) The princess slept until the prince kissed her. In (s I ) the event of the prince kissing the princess is taken to be factual, and the situation of the princess sleeping lasts until the time of that event. But other cases are more complex. Compare an example like (52):
(52) Anne will keep her job until she finds a better one. (52) is compatible with a situation in which Anne has ajob now, and never quits her job, simply because she may never find a better one. Clearly then, we do not want existential quantification over the event ofAnne finding a better job in the future. This situation is reminiscent of the problems which arise in the
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According to Bree, the implicature that the situation changes after the time indicated can only be cancelled if the until-clause indicates the result or the goal of the main clause activity. Bree also points out that there are no negative main clauses with result or goal interpretations in his corpus. If result and goal interpretations are systematically missing for negative sentences, this may explain why negative main clauses always observe the conventionalized conversational implicature that the until-clause marks the change in truth value of the main clause. Interestingly, this goes one step in the direction of Declerck's lexical composition approach, without postulating a full lexicaliza tion process.
246 Meaning and Use of not . . . until
interpretation of non-veridical before, pointed out by Anscombe ( 1 964) and Henamaki ( 1 978). Consider an example like (5 3): (53) They left the country before anything happened. We can accept the sentence as a whole to be true without being forced to accept the truth of the bifore-clause. That is, whether something actually happens or not is irrelevant for the truth of(5 3). An even stronger case arises in· (54), where the bifore-clause describes an event which did not take place: (54) Anne died before she completed the novel.
o
For main clause y: A.e[P(e) 1\ 3t AT(e, t)) and subordinate clause o : A.e' [Q(e') 1\ 3t'AT(e', t')) : llbefore(y, o)II A.e3t3t" [P(e) 1\ AT(e, t) 1\ 'v'e' [[Q(e') 1\ 3t' AT(e', t')) .... t'' :S t < t']]
This definition generalizes over both non-veridical and non-actual uses of bifore. For instance, it allows us to translate (54) as in (5 5): (5 5) Anne died before she completed the novel. a. 3e3t3t" [Die(a, e) 1\ AT(e, t) 1\ t < n 1\ 'v'e'Vt' [[Complete(a, n, e ') 1\ AT(e', t')) .... t" ::<:; t <. t']] This correctly allows Anne to die without her ever finishing the novel. The change from an existential to a universal quantifier correlates with a more general difference in status beween main clauses and subordinate clauses introduced by a temporal connective, which was already observed by Heinam aki (1 978). Main clause events are asserted, which explains the existential quan tification over the event of Anne dying. Subordinate clauses however, are presuppositional. As a consequence, existential quantification is not entailed, but only implicated. It is a general characteristic of presuppositions that they can be cancelled. The cancelling of the presupposition is exactly what happens in (5 5a), creating a non-factual interpretation of bifore. Although until does not allow non-factual readings, an example like (52) illustrates its non-veridical usage. If we want our interpretation of until to reflect the asymmetry between main and subordinate clauses, we can adopt the following generalized defini-
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We cannot infer from (54) that there is a time at which Anne completed the novel. The use of bifore in examples like (54) is called 'non-factual', because the event never materialized. The use of bifore in examples like (53) is called 'non veridical', because the truth of the sentence as a whole is compatible with the subordinate clause being false (without this being necessarily the case). In both cases, a translation in terms of existential quantification is not warranted, because the event described by the before-clause has not or need not have taken place. Landman's (199 1 ) solution is to replace the existential quantifier with a universal one. This leads to a generalization of the interpretation of bifore:
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tion of durative until, which states that the main clause situation will last as long as no event of the type described by the subordinate clause occurs:12 o
For main clause y: A.s[P(s) 1\ 3t AT(s, t)] and subordinate clause (): Jce [Q(e) 1\ 3t' AT(e, t')]: lluntil( y , <5 11 A.s3t3t' [P(s) 1\ AT(s, t) 1\ t' � t 1\ \ft' " [[-.3e[Q(e) 1\ 3t" [AT(e, t" ) 1\ t' < t'' S t' "]]] - 3s'[s' (: s 1\ P(s') 1\ AT(s', t' ")]]] �
The generalized definition of until allows us to interpret (sz) as in (s6):13
(s6a) asserts that Anne has a job that she keeps at some (non-past) time t. t includes a contextually determined time t', which, in the absence of a further specification is probably interpreted as referring to the speech time. Further more, (s6a) claims that for all future times at which she has not yet found a better job, Anne will keep her old job. In other words, she keeps her job as long as she does not find a better one. This clearly allows Anne to keep her job for ever if she never finds a better one. The modus tollens version of (s6a) in (s6b) shows even more clearly that finding a better job is a necessary condition for Anne no longer to keep her old job, because it spells out the intuition that Anne only stops keeping her job if she finds a better one. The combination of the generalized definition of until with the behaviour of event predicates under negation sheds some light on Karttunen's observation that not . . . until focusses on the onset of the event denoted by the main clause, rather than on its absence until the time denoted by the subordinate clause. Consider an example like (57):
(57) Anne will not quit her job until she finds a better one. In Karttunen's view, a sentence like (s 7) focusses on Anne quitting herjob when she finds a better one. Using the generalized definition of until, we can interpret (s8) as in (s8a): (s8) Anne will not quit her job until she finds a better one. a. 3s3t3t'[(-.Quit)(a, s) 1\ AT(s, t) 1\ ( s;;;; t 1\ \ft' " [[-.3e3t" [Find(a , e) 1\ AT(e, t'') 1\ ( < t'' s t'"]] - 3s'[s' (: s 1\ (-.Quit)(a, s') 1\ AT(s', t' ")]]] b. 3s3t3t' [(-.Quit)(a , s) 1\ AT(s, t) 1\ t' s;;;; t /\ \ft' " [[-.3s'[s' (: s 1\ (-.Quit)(a , s') 1\ AT(s', t' " )]]] 3e3t" [Find(a, e) 1\ AT(e, t'' ) 1\ t' < t'' S t'" ]]]
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(s6) Anne will keep herjob until she finds a better one. a. 3s3t3t'[Keep(a , s) 1\ AT(s, t) 1\ n s t 1\ t' � t 1\ \ft' " [[-.3e3t" [Find(a, e) 1\ AT(e, t'') 1\ t' < t'' S t' "]] 3s'[s' b;s /\ Keep(a , s') 1\ AT(s', t'")]]] b. 3s3t3t'[Keep(a , s) 1\ AT(s, t) 1\ n s t 1\ t' � t 1\ \f t' " [[-.3s' [s' (: s 1\ Keep( a , s') 1\ AT(s', t' " )]] 3e3t " [Find(a, e) 1\ AT(e, t'') 1\ t' < t'' S t'" ]]]
248 Meaning and Use of not . . . until
Clearly, the universal quantifier over individuals has wide scope over the proposition as a whole. This is what allows it to bind a variable in the until-
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c. 3s3t3t' [(-.Quit)(a , s) 1\ AT(s, t) 1\ t' s;;; t /\ \ft'" [[3e' [(Quit(a, e' )) 1\ AT(e' , t'")]] - 3e3t" [Find(a , e) 1\ AT(e, t'') 1\ t' < t'' :::; t'" ]]] (5Sa) tells us that there is a time t at which the state holds that Anne does not quit her job. The time t' included in t at which we start evaluating the situation may be identified with the speech time. We further claim that at any future time at which Anne does not find a betterjob, she will not yet have quit. This is equivalent with (5Sb), which states that Anne will only be out of the state of not quitting her job when or after she finds a better one. The only way for Anne to end the state of not quitting her job is to participate in an event of quitting her job. As observed in section 5 . 1 above, there is a general constraint on the relation between the state of affairs which describes the negation of an event, which requires that for that state of affairs to end there must be an event of the type of the predicate taking place. Using this constraint, we can immediately derive (s Se) from (sSb). Finding a better job is then a necessary condition for Anne to quit her job. The interesting observation to make here is that the sentence does not focus so much on the state of not-quitting as on the location of a possible event of quitting as happening only at or after the time Anne finds a better job. This is especially clear from (sSe), and it fits in with Karttunen's observations that not . . . until is punctual in this use, and is typically used to locate events in time. Clearly, the kind of examples in (sS) can also be handled in an analysis which interprets until as 'before'. However, the translation in (5 S) shows that it is not necessary to give a special negative polarity interpretation of until, or to build the focus on the onset of the event as a special requirement into the semantics of not . . . until (as in Tovena 199S or Declerck 1 99s). It is the generalized interpretation of until in combination with the behavior of event predicates under negation which is responsible for the meaning effects observed in relation to (5 S). Note moreover that the sentence focusses on the possible event of quitting in relation to finding a better job, and does not in any sense imply or implicate that this will actually happen. The examples discussed here thus argue against Declerck's strong views of actualization as an assertion. More evidence in favour of the generalized definition of until is provided by sentences involving quantified NPs, as in (59): (59) Everyone1 keeps her1 job until she1 finds a better one. a. \fx\fs\ft\ft'\ft'" [[Keep(x, s) 1\ AT(s, t) 1\ t' s;;; t /\ -. 3e3t" [Find(x, e ) 1\ AT(e, t") 1\ t' < t" :::; t'" ]] 3s'[s' [: s 1\ Keep(x, s') 1\ AT(s', t'" )]] b. \fx\fs\ft\ft'\ft'"[Keep(x, s) 1\ AT(s, t) 1\ t' s;;; t 1\ -.3s' [s' [: s /\ Keep(x, s') 1\ AT(s' , t'")]J 3e3t" [Find(x, e) 1\ AT(e, t'') 1\ t' < t'' :::; t'"]]
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(6o) No one; quits her; job until she; finds a better one. a. 'v'x'v's'v't'v't''v't"'[[(-.Quit)(x, s) 1\ AT(s, t) 1\ t' � t /\ -. 3e3t"[Find(x, e ) 1\ AT(e, t'') 1\ t' < t'' ::; t'")] ..... 3s' [s' 6 s 1\ (-.Quit)(x, s ') 1\ AT(s', t'")]] b. 'v'x'v's'v't'v't''v't'" [[(-.Quit)(x, s) 1\ AT(s, t) 1\ t' � t 1\ -. 3s' [s' 6 s 1\ (-.Quit)(x, s' ) 1\ AT(s', t"')]] ..... 3e3t" [Find(x, e) 1\ AT(e, t") 1\ t' < t'' ::; t' "]] c. 'v'x'v's'v'e''v't'v't''v't'" [[(-.Quit)(x, s) 1\ AT(s, t) 1\ t' � t 1\ Quit(x, e' ) 1\ AT(e', t'")] ..... 3e3t" [t' < t'' ::; t' " 1\ Find(x, e) 1\ AT(e, t'')]] This sentence claims that people don't quit their jobs as long as they do not find a better one (6oa, b). In other words, they only quit theirjobs if they find a better one. The fact that finding a better job is a necessary condition for quitting is perhaps most transparent from (6o)c. 5·3
Lateness
So far, we have concentrated our discussion of the pragmatics of not . . . until on Karttunen's (1 974) observation that the focus is not so much on the absence of an event in the period before a certain point in time, but on the fact that the event only happens after a certain point in time. This use of until implies that the event does indeed take place, but that it occurred later than expected. The intuition of'lateness' is illustrated in (9) and ( w), repeated here as (6 1 ) and (62): (6 1 ) a. b. (62) a. b.
*The princess slept until nine at the earliest. The princess slept until nine at the latest. The princess didn't wake up until nine at the earliest. *The princess didn't wake up until nine at the latest.
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clause. Of course we do not assert that everyone has a job she keeps. But we do claim for everyone who has a job at some point in time that they will hang on to it as long as they don't find a better one. This is spelled out in (s9a). For some people it may come true that they find a better job, for others it may never occur. Either way, it is true that finding a better job is a necessary condition for no longer keeping one's job (s9b). The most obvious choice for t' in (s6) and (s8) is the speech time, bur this does not carry over to the quantificational context in (59). Clearly, we want to leave open the possibility that people hold jobs at different points in time. This is reflected in the universal quantifier over t' in (s9a) and (b). For any such time t', though, it is true that the times t'" following t' will also be times at which the person holds the job, unless they find a better job at some time t" preceding or equal to t"'. Similar examples can be constructed with negative universal quantifiers, as in (6o):
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Meaning and Use of not . . . until
(63) a. Hij komt pas als je hem minstens honderd dollar geeft. He will only come if you give him at least a hundred dollars. b. ??Hij komt pas als je hem hoogstens honderd dollar geeft. He will only come if you give him at most a hundred dollars.
At least a hundred dollars identifies the lowest point on the scale which is sufficient to make him come, and the scalar focus particle is infelicitous with an expression such as at most a hundred dollars which identifies a maximum, rather than a minimum value on the scale.14 Given that the effect is related to the choice of values on a scale, rather than the character of the scale, it need not surprise us that temporal examples can be found as well, for instance: (64) a. Ik kom pas om tien uur thuis, op z'n vroegst. I will only come home at ten o'clock at the earliest. b. ??Ik kom pas om tien uur thuis, op z'n laatst. I will only come home at ten o'clock, at the latest. I fpas excludes everything below a certain lowest value on the time scale, it is incompatible with a specification such as at the latest, which refers to the highest value on the scale. I propose to extend this argumentation to exclusive constructions where the scalar character comes from other sources than an explicit particle like erst or pas. In the case of not . . . until the scalar character of the construction comes from the temporal connective: the time axis is just one example of a scale. A sentence like (65) presupposes that the princess woke up, and asserts that this did not happen at any time earlier than nine o'clock
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Intuitively, (6 1) stretches the duration of the state as long as possible, whereas (62) focusses on the earliest possible moment the situation can hold. In order to capture this effect of lateness, Karttunen assumes that negative polarity until t pragmatically presupposes that the event occurs before t or at t. The idea is that the time period beginning at t is the very last cut of the time stretch during which we would expect the event e to occur. In the present framework, we .can reanalyze this pragmatic presupposition as an instance of a more general phenomenon. The conclusion of section 4 was that the scope analysis, the ambiguity thesis and the lexical composition approach are semantically equivalent; they all interpret not . . . until as expressing exclusion on a temporal scale. We observed that scalar focus particles such as German erst and Dutch pas typically identify a value high on the scale, because this creates a pragmatically relevant set of alternatives for which the predication is excluded. Consider the following Dutch example:
Henriette de Swart
2s 1
(6s) The princess did not wake up until nine o'clock.
6. E X C L U S I O N A N D S C A L E S A C R O S S L A N G U A G E S 6.1
Problemsfor the lexical composition approach
Declerck ( 1 99s) treats not . . . until as a stereotyped unit with the meaning of a scalar exclusive particle akin to erst in German or pas in Dutch. His lexical composition approach suggests that the semantics and pragmatics of the stereo typed and the lexical unit are the same. This is not quite true. In the section on lateness, we already discussed examples which show that the use of erst and pas as scalar exclusive particles is not limited to temporal contexts. Konig ( 1 99 1 : 1 1 4) provides the following example o f a non-temporal scale:
(66) Erst ein Mercedes wi.irde ihn zufriedenstellen. Only (nothing less than) a Mercedes would satisfy him. The fact that nothing lower on the scale is good enough conveys the idea that the person has very high demands. As a consequence, it is pragmatically odd to utter a sentence like (67):
(67) ??Erst ein Volkswagen wi.irde ihn zufriedenstellen. Only (nothing less than) a Volkswagen would satisfy him. These examples show that the meaning of scalar particles of exclusion such as erst and pas is broader than that of not . . . until. This is problematic for
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It is the fact that nine o'clock is somewhere high on the temporal scale which suggests that we have to wait all this time for the event to happen. Thus the princess woke up late. If the use of until in negative sentences excludes everything below a certain lowest value on the time scale, it is incompatible with a specification such as at the latest, which refers to the highest value in the context. This explains the felicity patterns in (6 1 ) and (62) above in w�ys similar to the ones in (63) and (64). Thus the effect of lateness which Kartunnen observed arises from the scalar interpretation, rather than from anything particular about the negative polarity status of until, and it can be accounted for by the scope analysis and the lexical composition approach as well. Now that we have also accounted for the factor oflateness, we can conclude that there are no semantic or pragmatic differences between the interpretation of not . . . until in terms of scope, the one which postulates a separate use of until as a negative polarity item, and the lexical composition approach. The question arises at this point: is there any context in which we can determine which analysis is the right one, or are they all equally good? This issue is addressed in the next section.
252
Meaning and Use of not
.
.
.
until
Declerck's lexical composition approach, because he defines the meaning of the stereotyped unit in terms of the meaning of the lexical items found in other languages. Another problem which arises for this approach is that we do not expect the stereotyped unit to exist side by side with the lexical unit in one and the same language. However, this is exactly what we find in languages like German and Dutch. Erst and pas can be used to express exclusion on a temporal scale. As Karttunen points out, a construction similar to the English not . . . until is possible as well in both German (68) and Dutch (69).
In both German and Dutch, such examples involve full temporal clauses, rather than clock expressions. The (a)- and (b)-sentences of (68) and (69) express the same meaning, and give rise to the same implicatures. This confirms the close relation between not . . . until and exclusive particles across languages. It does not justifY a lexical composition approach to the complex constructions, though. If nicht . . . bis and niet . . . tot{dat) exist alongside the lexical items erst and pas, it is more appropriate to assume that English has a lexical gap in the paradigm. In other words, German and Dutch lexicalize an exclusive scalar particle next to the non-scalar only, but they can also conventionally use the counterpart to the complex construction not . . . until to express exclusion on a temporal scale. English does not have a lexical item equivalent to erst and pas, so it only has the conventionalized use of not . . . until to express exclusion on a temporal scale. In this connection, it is interesting to remember Konig's ( 1 99 1 : 99) observation that there is an intimate connection between exclusive particles like only and a combination of negation and exception. Compare for instance the sentences in (7o), and their representations in (7 1 ): (7o) a. b. (7 1) a. b.
Only JohnF came. Nobody but John came. (Come(j) t\ Vx[x E C t\ Come(x) -. x j] (Come(j) t\ --.3x[x E C t\ x� j t\ Come (x)] �
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(68) a. Die Prinzessin wachte nicht auf bis der Prinz sie kii6te. The princess did not wake up until the prince kissed her. b. Die Prinzessin wachte erst auf wann der Prinz sie kiif3te. The princess only woke up when the prince kissed her. (69) a. Maar in Italie hoeft geen enkele veroordeelde de gevangenis in totdat hij schuldig is verklaard door her hooggerechtsho£ But in Italy, no convict goes to jail until he has been declared guilty by the Supreme Court. b. Maar in Italie hoeft een veroordeelde pas de gevangenis in wanneer hij schuldig is verklaard door het hooggerechtsho£ But in Italy a convict only goes to jail when he has been declared guilty by the Supreme Court.
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(7 ra) claims that all contextually determined alternatives for x are identified with John. In (7 rb), we exclude all values different from John. The two statements are equivalent, and they both come with the presupposition that John actually came. As a further argument in favor of the view that the use of until in negative contexts is indeed conventionalized I would like to draw attention to a language like French. In French, we do not even use a temporal connective, but translate (72a) with the general discontinuous exclusive construction in (72b): (72) a. The princess did not wake up until nine o'clock. b. La princesse ne s'est reveillee qu';i neufheures. The princess NEG herself has awoken except at nine o'clock.
(73) Je n'ai invite que Marie. I NEG have invited except Marie. I only invited Marie. (72b) has a scalar reading in which the princess did not wake up any earlier than nine o'clock. But the scalar character of the exclusion comes from the (temporal) context, and it is not part of the semantics of the construction. In other words, the semantics of ne . . que is like the one of nur, rather than erst. The interpretation of (72b) can then be spelled out as in (74): .
(74) La princesse ne se reveilla qu';i neuf heures. a. 3t'[Nine o'clock(!') 1\ -. 3e3t[tE C l\ Wake up(princess,e) 1\ AT(e, t) 1\ -.[t o t']]] b. 3t'3t" [Nine o'clock(t') 1\ -. 3e3t (t" :::; t:S t' 1\ Wake up(princess, e) 1\ AT(e, t) 1\ -. [ t o t']]] c. 3e'3t'3t"3t'" [Nine o'clock(t') 1\ Wake-up(princess,e') 1\ AT(e', t'") 1\ -.3e3t [t" :5 t :S ( 1\ Wake up(princess, e) 1\ AT(e, t) 1\ -. [t o t']]] The fact that the focus particle associates with a time adverbial determines the temporal character of the set of alternatives. This allows for (74a) in principle to get the reading in which the time the princess woke up is nine o'clock, not any other time on the time axis. In this context, however, the scalar interpretation of ne . . que is strongly preferred. So C is set to the interval preceding nine o'clock, and the beginning of the interval is given by a contextually determined time (' (74b). The exclusive focus construction induces the presupposition that the event actually occurs. If we add this information, we end up with the formula in (74c). (74c) claims that there is an event of the princess waking up, but it does not occur before nine o'clock. Therefore, it must occur at nine or later. This is .
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Ne . . . que is an exclusive focus construction which can, but need not appeal to scales. Just like only and nur, ne . . . que is not limited to temporal contexts, as (73) shows:
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Meaning and Use of not . . . until
6.2
(Before' and (until'
One argument Karttunen ( I 974) advances in favor of his approach is cross linguistic in nature. According to Karttunen, Finnish is of special interest, because he claims it has a lexical item ennen kuin which corresponds to negative polarity until. What I found is that ennen kuin means before rather than until. The fact that ennen kuin is felicitous in an affirmative sentence like (75), which contains no NPI-licenser, suggests that it is not a negative polarity item: (75) Ennen kuin menen pitemmalle, selvittelen talouspuolta. 'Before I go further, I'll explain the economic aspects'.
Ennen kuin in (75) cannot be used in the meaning 'until'. Furthermore, the fact that (76a) and (76b) express equivalent statements does not necessarily mean that the two connectives are synonymous: (76) a. Kesti kauan, ennen kuin tapa vakiintui. 'It took a long time before the custom got established.' b. Kesti kauan, kunnen tapa vakiintui. 'It took a long time until the custom got established'. Paul Kiparsky (p.c.) observes that in contexts in which ennen kuin is interchangeable with kunnes it can be translated into English as 'until'. However, there do not seem to be any uses of ennen kuin which could not be translated as 'before'. Note that Finnish is not the only language in which 'until' can be exchanged with 'before' in certain contexts. The following English examples of before and until can be considered the counterparts of (76): (77) a. But it's going to be a long time before it is over its problems. b. Thus it will take a long time until the pressure will show results.
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equivalent to the interpretation developed for the English and German/Dutch counterparts of this sentence. Languages thus use different means to express exclusion on a temporal scale. French uses a negative exclusive focus construction, where both the scalar interpretation and the temporal character of the scale come from the context. In German and Dutch, the dominant construction involves the use of an exclusive scalar focus particle, which leaves it to the time adverbial it associates with to provide the temporal character of the scale. Finally, in the English not . . . until construction, we find that the temporal scale is given by the connective, and the interaction with negation gives the construction an exclusive reading. Declerck's lexical composition approach is not fine-grained enough to capture the similarities and differences among the various constructions languages use.
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Compare also the Dutch examples in (78):
(79) a. [De junta weigerde [de macht over te dragen voordat er een nieuwe grondwet zou zij n uitgevaardigd]] b. [[De junta weigerde de macht over te dragen] totdat er een nieuwe grandwet zou zijn uitgevaardigd] In (79a), handing over the power before the new constitution is enacted is what is refused by the junta. In (79b), the refusal of the handing over of the power lasted until the enactment of the new constitution. The contrast in (76) and (77) is similar. In the a-sentences, the long wait occurred before something else happened, and in the b-sentences, the long wait lasted until that something else happened. Naturally, the combination of a temporal connective meaning 'before' with a wide scope negation allows the interpretation of exclusion on a temporal scale. The interpretation of (8o) can be spelled out as in (8oa). (8o) Prinsessa ei herannyt ennen kuin yhdeksaltii. a. 3t3t' [Nine(t') 1\ -.3e3t" [Wake-up(princess, e) 1\ AT(e, t'') 1\ t � ( ' < t']] Not surprisingly, (8oa) is identical to Karttunen's interpretation of negative polarity until in (3 8c) above. Interestingly, we also observe that an implicature of the event actually happening arises in the Finnish and Dutch examples (8o) and (8 1 ): (8 1) X wilde niets zeggen over de verdeling van de ministersposten voordat de top van de liberale partij en de beoogde coalitiepartners zich ook formeel zouden hebben uitgesproken voor het bereikte akkoord.
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(78) a. De junta weigerde de macht over te dragen voordat er een nieuwe grondwet zou zij n uitgevaardigd. The junta refused to hand over the power before a new constitution had been enacted. b. De junta weigerde de macht over te dragen totdat er een nieuwe grondwet zou zijn uitgevaardigd. The junta refused to hand over the power until a new constitution had been enacted. I take it that the interpretation of Finnish ennen kuin and Dutch voordat involves existential quantification over times preceding the time referred to by the adverbial, and that they are in this respect similar to English bifore, whereas kunnes and totdat are interpreted in terms of universal quantification, just like until. The observation that (78a) and (78b) are equivalent is a result of the fact that their temporal clauses attach to different events. Their syntactic structures can be differentiated as in (79):
2 56 Meaning and Use of not . . . until
X did not want to say anything about the distribution of the ministerial posts before the liberal party leadership and the intended coalition partners had declared themselves openly in favor of the agreement.
until.
6.3
Implied durativity
One way of providing evidence in favor of a separate use of until as a negative polarity item is to give examples in which until occurs in a non-durative context, which contains some other NPI-licenser than negation. In such contexts, no narrow scope reading for negation can be postulated, and both the lexical composition approach and the scope analysis fail. It has been suggested that evidence in favor of a negative polarity use of until is provided by examples like (82), borrowed from Mittwoch (1 988), where until shows up in the context of a superlative, which is non-durative and non-negative, but a typical licenser for negative polarity items otherwise: (82) a. This is the biggest city we drive through until we get to San Francisco. b. This is the last meal you will get until we arrive. c. San Jose is the only stop we will make until we get to San Francisco. I would like to discard this argument from the start, because I do not think it is convincing. In fact, we observe that until is likefor in the sense that it combines
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(8 1) carries the implicature that X will announce the names of his new ministers as soon as the coalition partners all agree. We observe th_at the implicature is related to the notion of exclusion as such, and is independent of the way exclusion is expressed. These data weaken Declerck's lexical composi tion approach, because Finnish ennen kuin and Dutch voordat cannot be considered to form a stereotyped unit with negation. Still, they express the same idea of exclusion on a temporal scale English not . . . until do, and they trigger the same implicatures. Karttunen's claim that English until in negative contexts is logically equivalent to before is correct in view of the logical equivalence between (33) and (37), or (34) and (3 8). However, the fact that languages use expressions meaning 'before' in constructions expressing exclusion on a temporal scale is not itself an argument to interpret (certain uses o� English until in terms of existential rather than universal quantification. The cross-linguistic com parison of the expression of exclusion on a temporal scale provides evidence against the lexical composition approach, but it does not allow us to dis criminate between the scope analysis and the ambiguity thesis. They give rise to the same truth conditions and implicatures in all contexts discussed until now. This requires us to take a closer look at the possible negative polarity status of
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with a slightly larger class than strictly durative sentences, as wimessed by examples like {83) (borrowed from Horn 1970): (8 3) a. They closed the bridge until Saturday. b. John left until midnight. These sentences would not normally be classified as durative. Even so, the combination with until is felicitous. The interpretation we obtain is one of 'implied' durativity. The event described by the sentence entails a state which holds for a certain period of time, and the adverbial phrase measures the duration of the result state, rather than the duration of the event itself This interpretation is paraphrased in (84):
Dowty ( 1 979: 25o-5 ) discusses similar examples involving .for-adverbials. He argues that the phenomenon of implied durativity is restricted to accomplish ment verbs which have a reversible result state. It seems unlikely that anyone would try to account for the well-formedness of the sentences in {8 3) in terms of negative polarity. But note that sentences like (82) have similar characteris tics: they imply that there is a state (more precisely: a negative state) which lasts until the time specified by the until-phrase (compare Mittwoch 1988). Their meaning can be paraphrased as in (8s): {85) a. We drive through this big city, and we will not drive through any city bigger than this one until we get to San Francisco. b. You will get this meal and you will then be without a meal until we arnve. c. We will stop at San Jose and there will be no other stops until we get to San Francisco. Given that we need to appeal to implied d urativity anyhow in order to explain the well-formedness of sentences like (8 3), there is no reason why we could not apply that same notion to the examples in (82). If this line of reasoning is correct, the examples in (82) do not provide evidence in favor of a separate use of until-phrases as negative polarity items.
6.4
Other NPI-licensing contexts
If we cannot use the presence of until in comparative and superlative contexts as an argument in favor of the ambiguity thesis, we have to look at other potential triggers of negative polarity items, such as right monotone decreasing quantifiers (no , almost no ,Jew, etc.). We have already pointed out that negative
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(84) a. They caused the bridge to be closed until Saturday. b. John left and stayed away until midnight.
258 Meaning and Use of not . . . until
universal quantifiers such (86):
as
no one can combine with until in examples like
(86) a. No one quits her; job until she; finds a better one. b. Vx[[until x finds a better job] [....,x quits]] In order to get the bound variable interpretation for the pronouns in (86a), we give the quantifier wide scope over the proposition as a whole. This does not rule out the possibility of giving negation narrow scope with respect to until, as (86b) shows. However, this type of approach obscures a more general point, which is that other monotone decreasing quantifiers can trigger this use of until as well, for example:
Examples like the ones in (87) are extremely problematic for a unified analysis of until-phrases as durative aspectual adverbials. Basically, the problem is that we cannot split the NP into a quantifier part and a negation part, where the quantifier would take wide scope over the proposition as a whole, but negation takes narrow scope with respect to the until-phrase. For the negative universal quantifier in (86) such a lexical decomposition can be defended, but for cases like (87) there is simply no such option. Other arguments in favor of the negative polarity status of until are its occurrence in the antecedent of conditionals (88a), in rhetorical questions (88b), in the scope of too (88c), and embedded under predicates like doubt (88d), to be afraid (88e), and forbid (88D: (88) a. I'm damned if I'll hire you until you shave off your beard. b. Why get married until you absolutely have to? c. They are too cautious to expect real peace and dignity for black men until at least their grandson's era. d. I doubt that Ernie arrived until after midnight. e. Ernie was afraid to leave until his lawyer came. £ He forbade her to leave until the police arrived. Smith (1 974) admits that his scope analysis cannot handle examples (88d-D. As Horn ( 1 989: 348), from whom examples (88a) and (b) are taken, points out, until is only licensed in contexts like these if the sentence carries a strong negative implicature. This is true for (88c) as well. Horn characterizes this conventional usage of conveying a negative content as a short-circuited negative implicature. These examples cannot be explained under the scope analysis, becuse there is no
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(87) a. He bought almost nothing until she told him she wanted it. b. He invited few people until he knew she liked them. c. Sporadic protests from local organizations had little effect until June last year when Sheela Barse, a Bombay-based child-rights activist, moved the Goa High Court in Mapusa.
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scope bearing operator like negation or a negative quantifier around. Declerck ( 1 995) takes the data in (88) to fit in with his lexical composition approach, because there is a hidden negation in the context, which is necessary for until to be licensed. Although a conventional usage may be an intermediate step towards lexicalization, I have argued that a convention of use does not make it necessary to treat the construction as a frozen idiom. In particular, the literal meaning remains present, and the construction can be given a compositional semantics which builds the meaning of the whole from the meaning of its components. I agree with Horn's conclusion that the data in (87) and (88) motivate a treatment of until as a strict negative polarity item. Roughly the same contexts in which the NPI until shows up trigger the use of expressions like in years (compare de Swart 1 995 and Hoeksema 1 996).
I fwe take the examples in (87) and (88) to provide evidence for a separate use of until-phrases as negative polarity items, we end up adopting an ambiguity thesis, more or less along the lines ofKarttunen's ( 1 974) proposal. Although one might have preferred a more conservative approach, this may not be so bad, because the contrast with the scope analysis is not as extreme as it may seem. There are several reasons why this is so. First, we observed that our representa tion of Karttunen's and Mittwoch's interpretation led to the same truth conditions and the same implicatures for all sentences involving not . . . until. This means that English sentences involving not . . . until are semantically and pragmatically equivalent to sentences in other languages, which do not have a negative polarity use of 'until'. I have not found examples of German bis and Dutch totdat in non-durative NPI-licensing contexts similar to (87) and (88). This implies that there is no reason to believe that the German and Dutch counterparts to until are negative polarity items, so for these languages the more conservative scope analysis is sufficient. Thanks to the fact that the scope analysis and the ambiguity thesis produce identical results in contexts with an explicit negation, the analysis developed in this paper can explain why English sentences involving not . . . until, and German/Dutch sentences with erst or pas describe exactly the same temporal structure. The observation that narrow scope of negation with respect to until is equivalent to wide scope of negation with respect to before captures the similarities and differences between the expression of exclusion on a temporal scale in a language like English (which conventionalizes the use of until) and Finnish (which uses before). We can go one step further, and argue that we should let the different analyses exist side by side, because in this way we can explain why Germanic languages like Dutch and German have a scalar particle of exclusion, but also uses the counterparts to
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7 CONCLUSION
260 Meaning and Use of not . . . until
until and before to express the exclusion on a temporal scale. I n a cross-linguistic perspective, the scope analysis, the ambiguity thesis, and the lexical composi tion approach each make their own contribution to a better understanding of the expression of exclusion on a temporal scale. Acknowledgements
The research for this paper was in part supported by a fellowship from the Royal Netherlands Academy of Arts and Sciences (KNAW), which is hereby gratefully acknowledged. I wish to thank Arto Anttila and Paul Kiparsky for their help with the Finnish data and the members of the Groningen Pionier resarch group on Negation and two anonymous reviewers for helpful comments on an earlier version of this paper. HENRIETTE DE SWART
NOTES Vendler treats aspect as a property of predicates. Since Verkuyl (I 972) pointed out that both the object and the subject NP have a decisive influence on the aspectual character, it has become gene rally accepted that we should talk about the aspectual class of sentences instead. 2 How soon after the time referred to by the until adverbial the event is expected to take place depends on the context. As pointed out by an anonymous reviewer, the utterance of(s) implies that we do not expect the princess to remain awake until nine thirty. However, in the context of(i), a period of rime is allowed to go by before the wedding: I
(i) John did not get married until his mother died. People do not usually get married shortly after a closer relative died, so a certain delay is expected in (i). This suggests that what counts as 'shortly after' is deter mined by pragmatic considerations. l will
not provide more precise constraints on the distance between the rime referred to by the until-clause and the actualization of the event. Further evidence for the inference of actualization as an implicature rather than an assertion is given in section 5.2 below. 4 The # indicates that only a non-intended reading is available. In ( 1 2c), we can imagine Eve drawing a circle over and over again for three hours. Similarly, ( 1 2a) is acceptable if we give the predicate an inchoarive reading and interpret love as 'start to love'. Such readings require a more flexible approach to aspect, which allows sentences to switch from one aspecrual class to another. Such mappings are discussed by Moens (r 988), who labels them 'coercion'. As an anonymous reviewer points out, the sentence is acceptable on the reading which allows a continuation of the form '. . . but in other years, she didn't love him
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Received: 03.04.96 Revised version received: I 4.08.96
Department ofLinguistics Stanford University Stanford, CA 94305- 2 1 5 0 USA e-mail: [email protected]
Henriette de Swart 26I
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properties of the sentence and the inter pretation of temporal connectives, see de Swart ( I 99 I). There is an extensive literature on the interpretation of only, and the division of labor between presupposition and asser tations, which I will not review here, because it falls outside the scope of this paper. Recent discussions of these issues can be found in Atlas ( I 993) and Horn ( I 996). The definition given here is for event predicates in the temporal clause. The definition for state predicates runs exactly parallel. The main clause always involves a state, as usual. In order to keep the formulas readable, I simplify the representation slightly, and leave out the quantification over (dif ferent) jobs. As an anonymous reviewer points out, (63b) is felicitous if the person involved does not want to get a lot of money, and will only agree to come if you offer him less than a hundred dollars. These observations fit in with the analysis defended here, because this context implies a reversal of the scale. Mutatis mutandis, the same point can be made for (64).
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Bree, D. ( I 98 5), 'The durative temporal sub ordinate conjunctions: since and until', journal cifSemantics, 4, I-46. Declerck, R. ( I 995), The problem of not . . . until', Linguistics, 33, 5 I-98. Dowty, D. ( I 979), Word Meaning and Montague Grammar, Reidel, Dordrecht. Fauconnier, G. ( I 98o), Etude de certain aspects
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8
at all'. This is not the aspectual use of in I am interested in here. The view that negative sentences as a whole introduce a state into the discourse has important consequences for the analysis of negative sentences in narrative discourse, as shown by de Swart and Molendijk ( I 994). In the case of states like to be in thegarden, the situation must hold at all instants t" of the interval from t till t'. In the case of activities like to sleep, quantification will be over all subintervals t' down to a minimal size. Compare Dowty ( I 979: 3 3 3) and others for discussion of the minimal parts problem in the inter pretation of activities. Compare Kamp & Reyle ( I 993: 647) for similar remarks on Jor-adverbials. For the sake of transparency of the for mulas, I will usually leave out the conjunct which specifies the temporal location of the situation with respect to the speech time. This information is irrelevant for the comparison of the dif ferent approaches to not . . . until. Because Karttunen (I 974) is only inter ested in punctual until meaning 'before', I limit myself to a definition of before for event predicates. For a more detailed dis cussion of the relation between aspectual
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