The cybernetics of human learning and performance: A guide to theory and research

To EUzabcth, Amar.:la and Hermione The Cybernetics of Human Learning and Performance A Guide to Theory and Researcb Pr...

Author: Gordon Pask

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To EUzabcth, Amar.:la and Hermione

The Cybernetics of Human Learning and Performance A Guide to Theory and Researcb

Professor Gordon Pask

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TIt. Cyilm,,,,;a of JlumtlIl Lurnlng QM P"fo'm""~ manner ·1IIIcen.ainty/information IndioK·. In seneral. they are Joloetj". information Indices since Information i. p.ined by .. Iectlnglmonsst I set of liternath'os. The interpretation of thnc indioet depend. ~pon the pesis of the Iltemati,...ts in the unl"erse(.) conccrued.lId lipan tIM' origin of the p numbe!'1.

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All olemal (iJnpanial, IInbimed) oI:Iscrow may o....look "'Y'knl which in the: wi man Ite has defined; foruornple. the lI' pulw.llId OUtpUl1et of .... orgaai$In; ,timlll; It ~,.... Ind re5pOMn it emits. Fu,th .... be may <:(Impute 1M p numbers ill lOY Iymmatic mannet'o He could. for uomple. estimate them. by ~ng rlf he '""'" I Bayeoiln 11I'istiQ.an heoould do 10

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rationally) or. more often. be SIIh$cribeilO the common ltItiSli(:ol dictum that ... probability PI (thai x hal the value x,) is Obtai""'." the limit. for infin.ile W'I""""" length of the ratio Numb« or oc< 'lumber of """,m

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1M formlllation depends upon 'Itationarity' of thuource of ocamences (I notion considered further ill Chapter 2). RO\1sh1y. 'llItionarity' mul1l t hatlbe ulKkrlying stl'l,,;ture of Iht 1Oura! is unellanging Under Ibis interpretation. tbe UnttrtaintYlillformation ind", I,".M/ullce/ u"""'talnty/information meUu"', Oi~n tither method of <:(Imputing Ibe p numbe,s, any uncertainty information indiCC$ retlc.t ~lJ uncertainty/ infonnation about the optem. for .~ampl•. l ubscrlblng \0 the lut dictum. the e'temal observer may record .~nt OCQ1"encet: in a contingency table to show the freque ncy wilh which evenll tagged by valun or x (inpulltltes) and y (output states) occur. including the .,.. nll due to joint occurrences. Th. tIltric. in the oootingency tabl. m.oy nOW be taken 1$ estimatel of the actual probabilities (I good onmple il &i'en ;n McCiiU (1963) who also provides the marbcm.otiQi apparatus needed to COIPptJle in \er1llS of counl numberl without tJlnsformins tbern into p numben). Some ilUta""'" of \hi, type of calculation ..... ci!ed in Cllaptcr 7. N.~t, an cxtem.ll obKrver may presuppose llIat lOme olhcr ~'er (a puticipant.lila an operati.... In industJy. Or an experimOO 10 litis enviroom"" pr",ide .. timates 01 its ,viabiIiIY. compl"';ty. regt.llarity. or wba~ (dep"odjn& "I"'" the cboseo Il>dc~). from the putici!*ot', poiO! of view. Some uamplel of targe-orp.OiSlltiOll task... lIIlysis along tha0...,. in Table 1 ""d Fil- I . Similar Itudiethl~beencarricd out M

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F''!fUff I lnfonnation ... tyolo fo, ,;x ind"'trial/(Ommcrtiol tub A. S. C. D. £, F. Upper <:IItve (oppr"l'
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in the 1Im\)(r Industry by Van Oldt (1971) who «litH the indioellc ergonomic and work . tud ylllUJurementS. S!&ni.land (! 966) 1Ia. u!led sim lIlt techniq .... in COI1IIOCtion with laboratory tasks and hal dco;iK
J SdK'tf.-. OJlft1lIiom and Sd«1hr Work

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7 Confidence Estimation Consid.r an "rnl who iJ; a senticnt bein, (a mao or possibly a macbiM Or an Inimal) able to inl.rpret and DDfUptchCfld. lan~age in which questions CIJI be 1$Iu:d. The vol)' mtriCled fannal IaDguagcs o f \he last ..aion CI.II be aupncnled (II in lbe Scigmann and SIO.pielOIl pa.pcr) 10 M1"Vi! in lhis capacily. [ .1Ia11 u ...... Iurallansu .... in order to gi"" uamples; in fact, some intermedille oompl.~ily of Iln,uage i• • mployed [or much of our turreol work.

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The ".. nl (J ..ked • multiple-choico l)'pC of qPHuon. Syntactically, il il

an exclu,ive disjunction O[ , lal.=nll. Bu! these ltalemenll have. semantic in lerpretalion whereby Ibe agenl rcl"crslh.m to a body of i0 I.rnal or oxterM! data and the question;. pre[Kl:d, ...h.o il i•• ddreued, by l b. '~iTt=1 U> I4lisfy a relation (whicll il 0 ... lIIW"Iiog of the nuony·fa.:eled aDd on.n misu.ed word 'goal"). SlIOCi!lClly, • question of lbi.1ypc pt>ICS a problem; to Jiod (..y) the one and only OM .Iten>ati,.., amwef, .. tisfyiog the ••latiOll 'bridge-building .ngineer'. within 10 inlerval, <1t (which may be inddinite), given I Rmantic interpretation o[ lb. language in r.. peeI of indu,trial history and the following allernati .... stalemeou : (a) 'Brunei buill the Bristol Suspension Bridge·, (b) 'Step/leninn built the Bristol Suspensioo Brid..', (e) 'W11:e6eld buill lbe Bri'lo! Suspension Brid!'"·. "!be semantic inlerpreuotion admits. for .>llJlpIc. such faetual data as: 'the Brislol ( Road) IU'pension bridge ..... , buililry an cop""r who buih .. ilways· and 'W.kefield built no /1Ijlways' and 'Steph.nson did no! de>ign Temple Meads SIation al Bri l lOl·, , uch inferenccs u ·Wakefield did nol build Ihe bridge' l od 'ifit il true l hal Ihe bridge wa, bulJI by an engioce. who buill. /1Ii1>....y to BriMl then it i. not false lhal Brunei built Ibe suspcnsi<m brid!,"'. The pragmatic io!erpreution ha, u imperative,! iDlerropti .... put (I qDCStion 0( this kind il ioomorphic with I command t(I aDS"....) and it lpec:ifics the .... lion d«med .COI"feCl' (na"",ly between , oadbridges and bullM,·~ _J).II is improper 10 gloM lh. ios"" by co .... ceiving Ihe q ueslion "" Ibe Ilimulul for a correct rcspome, ..... n though !hi, idenlificalion i• • uUe.ted by Ihe usual namely:

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I. l nilially; 2. aflor .. mpliog bdi,fuboul fac1U/1) .lSp«U ollhe prodlX'l Mid; 3. af,or uposure 10 ad .... tiJinB in favour of a new prodUC1: 4.• ft •• an .1~mp1 '0 ~nfum the chaoge of opioion; 5. oft.. IdvmQ.iogln r,"our of th. original (nolth. ".w plodlX'l) Ind: 6. after trarning in r.,~ of factual data with corr..,1 or millak.n 'blo ... lcd", of mulli".

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Th. last (Irainins) opo.ation i. i"se.ted to check lhal the measum! 'un. <m ainly' i. I qUlnlily that iI, a. it should be, reduced by the """.ipl of objeeti,·. information. Opinion change in r..-our or lh. " .... produ" i. deorly perpetuated ""On though the origina.] plod.,CI il ad"eniS«! (the products an: ,Iunati"", for all ptllctieal pIIrposes). In Fi~, 10 the: order of presentation of mallriall (4) and (5) il reversed. Under th""" COiIditionl (oo immediate ooofinmtioa of tbe DeW pcodllC1 hypo1besil) tbm: "appreeiabk opinion change io favour of the original product. H.DCC, tlIm: ill ...."ttSaJ. Since tho _ prodlX'l .."....w;nl hili IlOl t.«.. ~nfumed, lbe Pmnltatioo of data Cavouriol the "'IKbu>J product lead. to In ambigllity, Wt is resoh-.d by 'e'lmion to tbe original

10

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A 11I00re1lCI) Poilu about Information and Its Measure.~

It i..... 11 kno ... n that the mathematical form of .. p....sion used to represent a selectiv. uneerlointy/information ind.x mirrors the mllhemalica) form of an 'nf"'py: Ihat ii, Ih. ph)'$iOllI quantity which inc ....es over lin", in I physical dosed usembly as en ...sy;s d.graded inlo leli speciJle and uSible forms, fOf <:.llmple, in lhe OJX1"'tiOIl of a heat engine Of the metabolilm of a ~JJ wkm: "''ee COlOn .bout because. al a molecular Itvt~ \he increut in ..,tropy caD be expreaoe;sion ofcnersy Or degradabl. m,uerills,l""h al' food$l lIIf. Brillouin mak .. a distinction betw~n 'Bound Information' CODCCrned with the configuration. of • ph)'lic.1 .ysltm and 'F .... Inform.tio,,· concerned ... ith tM possible cOn' figutation. of. n ~~lmcl.y>t.m h.ving no spocially phy.ical interpretation,

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'17Ir Cybmmlu of H''''1tIn u.".IIi1t& aM Prrff)mURIN. IppraprillC limiting principle il rumishro by Br<m~rman'llimil (Br<mmorman, 1962; Aohby, 1968) , Ta~e any physical un!>..", you like, whore po$I.ulates 110 S Ipply, It i., by lhe definition of'physlao! uoi.-erse', iiolltro Ind, by il$ 01""". lUbjt<:t 10 Br<m.mCfman', limil; hoDel<, il i.. if IIInc poslul.!-S apply, . mlchine ofthi' type, or 0 bag or Ihem which i. illelf a machine of thi. Iype, I n partieu lor . any ,tal (en gi necr '1) mochine i.llnachi ne of Ih;' (l!>ItnICI) l)'pt, II i. wo"h IIOling thai though I ..,pcct lhe ulililY ofl""tulalt$ t 10 S and lhe ctegance of their de>'elormenl, I do nOI .. gord lhe~ pri""iple. IS u".,.aUy Ipplicable or '1nIe'; nor do I OOllCUr in the philhlOphical oon, duoion aboul the uni _one Or isolalll!d bill ofil, HOWC'..... il ;1q uile importanl 10 ,Ireu Ihal my dilagreemenl il not based on vou nd. directly related 10 lhe nexl (probablillic) dcvdopn1(OI of machines.

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:," : . ) on hllf lilt octuion. the seleclod sla le would be z, and on half:, ; a (aea.pre ... d by awgning a posilive fnetional number. p. 10 lhe ,lates •., z, wilh the prop<"y thallhe p Dumben...", 10 uoily ud 'latio, 'p(zJ .. p(:.) .. 1', In Ihe jjetlorll case of '" alternatives /lamed by Ihe .olue of an index j, lhen p(z,) .. l/m. In $0 fa, al thi l metrical lI~niDn tallies wilh th. freque~y oounl, as lhe number of illSlaDCCO i. inc...ased, p(:,) i, 1M probability of : , {Ind rt'm.Iins $0. c~n if p(:,) ,,"pam from the ~uiprobabil ily oondilion Ihal p(:,) .. 11m for . 11 valuOli o f j), (d) Furlher. under Ihe lame restrictionl. Ihe condiliona l probabilily P(: A:,) il the: probabilil)'. gi= lhe machine i. in stale:, II ~, thai il will be inSla'.:,alinllllm7+ I. (c) As a refilltmen, in machine design, il is po"ibl. 10 as",,,, for each z, in Z a conditional probability p(:~:,) Ihal • certain transition witJ OCI:ur. Thillrick amou"u 10 usinS a 'j'!lcm..tiaolly biassed random >OUTCe or 10 bialliaS unbia utd random
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Such figure. 1110 l impler 'e "",nipulole. fer.lI practical purposes, liIan , tate representalions. Th. main juslificllion for talking, improvidently, of "0 U:5 is because a lIa t< re pl'Hl'nUl tic n i, m ore .u ""'ptible to logical InM l)'lis. On. way ofl"'\ting the malle, is to nOle that on F'SM can be rtprded, in its .tate rcprocntatien, as the 'grammar' or ·.. t of rewriting rules' (lilt of q""druple<) aDd • fonnal lang""!l"' Lepl npm:sioM ;n thil fnrmal language are IUd (l)'IIlbollO input ltale) from lh<: machillC inpul tape l lId a ... printed (symbol to OUIPUI StaIC) on 10 lhe machine oUlp.n tape. Tho internal 5I.les an: non_lermi ....1.ymbol< in the language. T'hew Uf,lemcnts Irt couched in the It1n\inolos,y for thot part of psydIoIinll"i.cia concemed "ith phrax 'lnIctUrt. g:r;omman Ind the n •. The crucial iSS\le i. the ui ..e".,. of ••tatc.l ....ymbol corr«pond
For """"'pl<, FSMI, n I diU. compute only 'Wu. ... p""';o ... ( KIce ... •• theomn), Because thaI is SO. !he otllerwi.. arbitrary idea of an OUtpUI pint lu I>SIaDCC. " noD-Uivial OUII"" occurs if, and ooly if,. machillC hu rccosni$Cd (in otbtr ...'Otds KCepICd) ••!ring or uptnsion belonging 10 lOJIle elm: in Which case it il I l'tCognisn of that class of e~pIl;$1.iOl1S. Further, the irredundant inlem.1 l!atcs of an FSM are IlOI jus, mechanically o rdailll:d configuralion. but co ...... pond to hi.tori .., i.e. 6nite . 'preMionl, that \11. FSM i.able 10 rtCognisc. The .. rious re.der . ho uld refe, 10 Min.ky (1%7). Chaplerl I 104 conllin the ma§! ."ilahl. I'eatment of Ihe con~pts I ha". jusl mentioned . The development of "'achille t heory in lhe: field of p'ycbolinguilticl i, brilliant bUI hal questionable relevance.' Olle compact acco~nt of lI1lI.hincs U grommm and of lhe: .~pus.!ions t hey •• n genente 0.- accept i, in a tmOS of papen by Chomsky Ind Miller (in lute, B~sh Ind crollant .... 1963). It is weU worth rt'ading thtse articles alld also the Ihorter la:ounl;n Bach (1964) of whll .. pmsiOflS can be produoed{acceplCd by whOlalion. of Figures 11 and 14 tognber wilh twO additio ....1 .ymbols: namely' , 'tOltand for a pa,,*mell;coptralion upon the intmtal

,tate .. I o f a machine and . ~ . 10 , I....d foraM
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'I'M CJi-_II<J 01 H...."" /.umlnt OM P~'lo,,"'ma (b)SimiLo, ""Dlmen" apply 10 a TM 'I"" ""nlputin, macbl....... d il> s;rater pov.-n moy be.scribed to itf "cater slOrage capacity; for eumpk an FSM canDOt m~ltiply ofbitrary numbers. But of """"", it II possible to WItulale a finilUlction; Davil (19$8) bases hi. apJ"OIcb 10 r.cuni"" COnlpUl. f~nction Ih«Iry in term. oFTuring machines ralh .. Ihln t .... ,..,'erst. (0) Nut. the,.. is a uni"erlal T uring machine T U (in FaCither. a'" indefinite numbers of Ihem) able 10 compule any function Ihat can be cOmpuled by $Qme TM , The '"lilt i. most con'~nienlly stated, for the presenl purpose, in lhe following mIInner. Any TU is able 10 aco:pl Ihe lap< description of any TM and to """y oul the o;omputations thai would be porlormtd by this TM. A '18p< dn<:rlplioo' mi",1 co",,>! in an arnngemeol of tbe quintup1eo ~li1lg lbe TM io qucslion. 1\ is ~, COIlve",ent, _lid for SUbstq ...OI dc>-dopmentl il iHs""nti.r.I, to
(the oripnal d..mpcinn being demolished io lbe pro«:I'). Nexl. lhe~ if, from lhe uil~nce cI TU• • flU'1ber lIIadli,," (called C"I'Y .. a tag ",ord) lbal will copyany description web .. lNw (TM) to produa copi.. of it. Thai" C"P}" t o..>er(TM») _ < o..rr(TM~ I>trr(TM)}

(the oripoal deoeription beins demolished in the 1"0""').

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2. In reopoc< Napt . 1Id Nl< I>0oI< ,lid po<WMl<s' ~10CIIUl0". which. Ukf"1 rll<' ,I>< a'&W""" in "'" nu' '01."". Qr ,he oluli<>lt pl,_ltI
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A uniwnal c:on.tno:tor.

F"uI&Ily then: is _ ""nlroller machine. alsoa TM. which i, ablt to organ;.. the aC\i,iliti of Build_lid C"I'Y in respect of ik-'CT(TM) ,"'lUch can institUle lhe following operlltion (using the ""l8lion of Fig. 16. ill fig. t 7) • C"I'.1{lIt..... ITM)) _ ( lIn>:r (TM). 0..... (1";\1»

BfIi/J (lit.... (TM» _ ( T.\{. lit.... (1";\f))

al Ihe end of whieb TM and ilO dtlCriplion arc cui free

by punctu.lion.

C. II Ihe .ntif!: machine Til.; Ilul\ i, TfI.. ( Copy. CO""o!. &;lid ) 10

thai

TfI.(lItsrr(TM» _ ( TM. Dm,(TM»

and Til. il pr ....... ed. lbtrc i,. dtsmption clTR, TM nnd TU.

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(1966) ICClUK S alld thi' m(~1Ke (not only ICClun: $ but .11. at 1e.,I. a( part 1 of tho bonk) should be""nlul!ed. The entirety TR il a Von N.umann •.. If·~ucing· mlohi .... 1Id il ml.y be formulated in ,'arioul way' 11\10, remo'-e the 'linearity' (Von Neumlnn', ",'oro) of the I8pe descriptionl [Nur (TM). One of th~ .. ways, the T .... lalion model (i nlroduced In Par! 2 or Von N~umMn, t9(6), i. di,cussed brieHy in lhe ""~I chlp ter.

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of tho ·dcc;';o~ rules' of the individual lutOnua.). S~rely I prerequisi te of ..,y group ·d.cision rul.· ,...... in!< individnalaulomaa.. But a simple a"e"'S" 'qlW1tity of food' doe. Dol ..em to he the m",' impora.nl (actor. Ind il hOi booen 1It",,'n that the dirlribw.1atI of (ood. ""thin the .nvironmem Ihll the con· figuration iohabiu, i. umalty more oignifiClM. The dillribl'lkM as senxd by the outermos, lutornall does nOl always irnticau: the quanti,y of (ood w~;'h "" ultimaltly he collected by lhe compo ... nl lulomoll. Sio,," .. "able confipration i. ahlt 10 compete or """penle wil~. or engulf, other collfipra'io'" of utornaa., • food distri. huliOll primarily ind,.,.,.. the •• i".noe of another configuration. Ralher ex'."';''e uperi_nl$, .... mining ,he relpo_ of collfig" ration. tonrd. deliheralely inuoduoed coIlectionl of "nviable aulornaLl, emplric:ally "'ppotted the COfIlention Ihlt inci~nt iMIa bilil1 in I configuno· tion is due to lack of I componenl (I ~ of clemmllr)' ."10....1011) and .ha, the configuration has. 'rwed for' and I 'goallo IHI'Ch for'lhis I:ind of compotlCn, (Pask, lewil aDd Feldman. 1965). For .... mplc. the mi$$in~ compo"""t may he Iype A 0 A 0 D: il e0ll1d he oblained by engulfing. It:M .table collfigW'ation "pl.tt with this Iype' or by coopotation wilh il. Thll1.lgh this ' .... d· ((IIIld be: upressed in LmnS of food di$. lribunOM that is 001. in fact how il i. dlurlbU al the conJiguration Ie.... ]; here, d.!Criplion. If. in terms (al le.,t) U oomplu U the chslluleri,tic action !"'".rn. of .utomaton types, R.sulu fTom on. of the simplest c'perimcnls of this k.ind (th. ",,,,,,lIfJ1t of a specific change) are shown in Figures 28 and 29 (I control experim.n t) using tbe Iype /I mod.l. Tn a free .~nnins simulation, mechanisms of the ki nd propooed appea r to be responsible for a number of ubiquitous pben<>mena. One of them i. shown In Fig. 30. h ma)' .ilh.. he Interpreled a. a predator prey interaotion, tbe population phenomena . n~ly~ hy K.rner (1 959). or iI$ tbe •• plicit symj>1om of a primili". immune ...ponSl/, notably io tbe Sl/OSI/ of Bell (1913). Cerlainly, tbe oocilJatory interaction ClO be: s"ppressed by actions thaI art designed to denlily r~ullle the reproduction of tbe configuration """,rjr""nr. """nting 01 prt)' or the conjip'grlfJlt counting as In alien organisation. l.S JWrnspeflI~ IdcalifieatiOll Suppose that the IUNe ooofigunolioru of aulomaLlan: identified II the reproducing/C'VoIvingtntities. (.... p
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D bd""l: to .nother uni"", .. U,. n..... i, a function. or in gerwnl a relation. F. curying .Iemenll ($IIclt u II) in its dom.in, into elenwnll Bin aHIomain; lik""'; .. a .. lation, G, c:a1T)'ing elements C in il$ domain, wo .I..... nts D in its 004(11""0. anal"ll)' CJ.isu in 10 far u tbert is" ..larion becW«ft F (in the universe Ui) and the .. Loti"" G (,n the uni~nc [I,). n.. analogy ,urri<'t if .his .. lation is an isomorph"", or a homomorph;'m. n.. 1lM/"Il/ml uni"",.., is oplci6td by ohcosin! an ,ndefinile Ie> q"""'" cf properties Px of V. arid P, of UF; tbe analogy MS no neurrDl proptrtit'S and is d~Jtd if far all P" 01 P, tbat are .. bted by tlt. analou undmyin. the Iheory. TIle limitation upon 'tuning' is that this 'DllIog)' .. mains al'll'8)" .trict, or 'turu",' is carried OOt 10 IImtR this n:sult.

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compooent of the rtgulirtor (u in Chaptu 8) and are ... p... sentro, i$<)mor, pbically, in the model (al in CIla~ ... 6). The construction also indicates I~e u:wictln1tJ imJlOf'td upon 'hillin,' in genff'll; IUmely, it mUiI be open to insuumt'Dtarion and representation within tbe calculus of finite-function ..... chiDes. In tl,lnt., lhillimltation imposes mtrictiom upon tho oize and ..ructUrf! of the (large) ulll...ne '" in which the pheftomena of inktnt can beo~.

6, TItc point can hi: uSllfuJly tepltrased, using a distiDction due 1(1 Hnse (1963) di..:~ in "uk (196), 1971al. The distinction dtmarclles ."'logi .. ...ilk ud M'iJll()ul 'neutral' analoginJ properties; IMt is, propenic! of u nlkt.rmined ...1..... n~,.t some in.tant. A 'tandard Inolosy il a rel.tion, in the simplest ~ase, of th. fo'm 'J! i. to Ba, C i"o D' whore J! and Bbdong tooneuni"orse (Vz .oy) bul Cond ~

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direainl: .nd leaminl: Cln be aKTibed to a mlibegollen choir;e of lbe unit for obltrvation. Inllead of regardinl: the IUbjtoct .. " I)"ttm (Iuch II a s)'$Iom in eLossi",,] phyQct), witlt input and output it would be ponib1e to r.gard him (now him quite .. rioully though) as a unit of intttp"'l.ltion;" symbolic "rueture whick is UI U"lIy executed in a non· localised pro"". ",r. R.ally, il is" matter of approach. For, in either calt, the Itntient characttr of. kum.n being (and olhe, >)'Items as ",.11) must be .oknowledged. Either hi.lnt.yily .. " symbolic (intorp1'l'live. innovati~, $tratcgy COJUtruclingJ entity can be taken asfundanwmal and the processor mponoib!e r<eoyliied anef Ihtu; or else, using tbe apprDaeh $I) f.r adop~. the prooesI(lr can be regarded II tlte fun
R./ollolJm

TIl, CyM"'tll.s of H"m .... """nlnt and PtTfwmanc, e<"nt' rat~r Ihan someOM c:onccmcd with buman ncu.ophysiolOS1) and to ~ tMI man i. 6rlt and foremosla.oymbnlic ent;'y. Somelhing i. gaill¢d by doiog so. Under 'his interpretation il il dear thaI tbe ""nstant conditiON ofllll experiment .... t upon CC1tain norms ",hich I ~ .ubjcct a=pts if be engages in a.n uperimenlal oonuxt (to take pari in lhe e: (OIapley i. maintained by a oo<ml.ti"" ..:hem<', I~ • .Is and interpt<1t.o. ,ok ""hi~h lhoe regulator musl 01>0 ;n1ttpret. For ita part, lb. ttgulator cooperates ",ilh Ibe subject (Ihrough tbe •• perimtn llll" ngua~) and make. it fOJJi/)/~ for him 10 keep tbe oontracl he has agr«ey "' more interesting hypotlitlt> are ICSttd, t/tat hoe is loolcing al a conve .....tion in which the subject and !he ttglllator regard OM .""lbet '" ·~u· Ind 'I' (Ml, U befort, in which thesubjea reprdllhe ttglllalor", ill. In the ma.t restrictive forms of tbcoJy, Iheac points Ire 1101100 obtrw.i,~. One reslricted (onn i.lbown in Fig. 34; the features of ",1Ikh are list
(b) H. (2n ",,/>, or<.Ier e'~nll al !be cost of rntrictin& bi . ctlquiry ,n<.! he i. not in • position 10 order All • ...,nts taking p\Aa: in lbe joint ' )'$Iem. (e) The ,pedal environn!ent;1 lymboHc and i. ;nterpn:Lable both in lhe object language of tbe experime nt.nd the ob ..,,'alio ... 1 nlelalangu"ge. (<.I) E.'ents (trannetions) in the sy.tom are only di.linct from tran,...tionl

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in ~ o",,",,-alional mtlllanlUase in SO rar as IJS38e at lhe object lanpge i. ~Irictcd for thi. ppeCial (l ymbnije) environmenl that embodies the obsm~r'l experimental h),polbclil il diocin,wshed ., the 10piC of. oon'....... tion whidt the regul. tor and the subjecl di$CU$S. (f) The obocrver colerlll;ns hypolhesctt about relatiolli lhal may be broIl",1 . bout by lhe eMCUtion of prooedures and the lopi" t/tat m.o.y be known by dint of e~e<:uling o ther procedures. Some h)'potheS<$ conerrn knowable relations and other. concern how rdat ion. are known, reecn· IImeted, .n<.l ... tisfl~,

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that the anQ!ogy underlying the thoory i$ nOt ,,1....aY' wiel bl>t only 1~lIy "r;c,;. i.e. Ihe ;'trV "" Y". For uample. lhe ",gulator in such a 'y>I.m could be alKllhcr human being; For ill>\a~. the: obocrver himsclF, In lhal cas •• il i. c~a, thallh. olR ..... , would be a p""Ic/l"'nl,But by the sam. token, th. apparently ext.rnal 'tuning' ope!1ltiol1$ to II«'UrC co~allC)' (and to mainLain transactio... ["""If(! (m the symbolic cn¥ironmenl) abo con~ lhe obsc:r.'Cf inlO a participanl 'peakin& in lho object langwoF. Eifcctiyc 'tllDing' i, "",I really an u'tr/.111 opc:r:otion and til< observer i. no 10ngtT an ~%'(T1IQ/ observer. As an altemati,.., the obsc ...... ClIn maintain hi. Il.Ilu. I. an (%'''''''/ obse ..... r but only hy tolera~ng a theory which il unckrpinned by an analogy lbal il/ocolly Itrict but not """"Y' Or al aU inl.!anu ,trict. w. deal WIth prob/lcml of this !)'pC In Chapter I I and air", ..ver.1 compromise solutio ....

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1.4 TransJt""" from Rolatiristi< \0 R.fttctl •• lbtGrlel

Whenever tho

..= ! obser.n·s position is abraded. tllc theory ud tl>c methods and mod.ls associated with II, \IecomeI rtft«llw. 1M dll.tint;tiop is nOl U ckamJl in 1110 ease wl\en the obsttvtr tI.C!s to maintain his .... terna! .Ialas bUlto relinquish the potiibitity of In .l....ys strict und .... lying analogy (so lhat cerlJlin "".nU arc Itrictly mealutllblc, qUllntifiable, etc., but other! arc not). In Fact, .. preo.io...ty....:md, there i, a continuum 0( poMfbilities. &>~ bave httn insltUmrnttd (Pul<, Scott and Kaliikounlls, 1973; Puk alld Scott, 1973) and an: 10 be described in the nat volume. ill a rule, a point il ~~~h!ld at which the occa.sions upoon whi~h the undC'rlyi~g analosy is 1"""Uy strict become so !1I/'e that Ihc th.o~tiCllI comtruct i, virtuaUy u.. l0", and, . 1 thil point, adoption of I ~fI«1i,. theory illnc: only ,"nsible option. It should be streoKd that ~1Itc(i'.. lheories an: perfectly respectable and can be cklllt with in tilti. o,,'n right but the:)' ;nYoI.'. diff(KJlt .~ptfi. mcntal techniques (to be diKII=d Ind .umplifted, . pi n 10 th. n.~t volum.) .nd havt little u$Cmb~nec [0 clmical theories. For fUIUK ~fcrenoe, it il worth nolin, here that alianlficant tn.nation takes ~ at the point .... ben the stnIctllre of the Iymbol;': cp';ronmeJ\t (Fig. 34) u.nd .... II\e control transactio... in the joint 'Y'~m. i.•. when the dialngll<:;' no longe' confioed to • topic (ho~'., broad) but the topic .vol,., . under the innuence of the dialogu•.

comes

to dl.pel thc imprC6Sion (which may .osily h.,'e httn given) that the .. only apply to human subjects. human learning. cognitIon allll so on. In ~holo8Y, tllo biu is,hiftina from behavillWillic 10 symbolic and cogniti~ intcrprr1atlon.; for e~ample. 1110 t",nd exhibited in &andu." ([970), A 'i milar tranlfo.mation i. taldng pia.. in ethology and fOCi.1 anthropology. 0111: maniFestation of tbe trend il that .vent.< pcc'ioully "'garded II epipbc:lJOJII(na thrown up by the compkx a"..pl.ltion of an und .... ,yin' panicula~ prom.. an: tofIClOl.-.d nowadays IS .ymbo~c "'Iulatory mechanisms; . point of .i.w that goes (rom lhe whole to the pa.t (Iix. ulatl,'lJm) .Olhc:. tban going in lhe traditional direction of PiIrt to whole (one .. Ii"", Feature oftbe cla .. ical theory). LD his dileUwon of populltion dcnsity control, Wynne Edwards (1963) put.< fOf'll'ard a convincinl argulllCllt that many p/lmomcna of display, mimicry Ind directive beha\'iou. ha,~ . Ipttific siplalling fur\Clion, Rille. than lIoing biological .p;phenom.na. They mediate commu nication in a Ipttific denaty control l)'Item. For .... mple. tbe singing and «mterio l consi
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condition is that the WI>ef'. OIIlpul tan fonn. oon.olUllericiocd rutty inl""l0 the 1eaCh..- and, vic:fc versa, tn.t IIIe teacher', oulpul eao fonn a oon.ntuJ>ericiocd fllUY inplll II, IIIe learner. II wiU be cvidenl IlIal 1M ",.ul~", .)'Stem i$ distribulod; IIIero;1 no runCiion.! diSlinction betwtcn the Iea.her and the ~arner. Or, 10 lOlIi:e I point also voiced by Von F",,"'or (a nd which i. gtnorally valid) ItDmlng entails. J~",h" who I~Q''''' Just te'ChiDg entails a learner who lo .. nl. ,,:ny theory or learning in the prcferred Ie"'" is a theory of teaching. and

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The Cjwm~I/'" ~f Hu,""" LnJrnlng DM P'rfo'nwn~ prexn! rorm ,be objoctionappli.. only to lengthy experi ",enl •. With h ulI\An •ubjecll though, if • more fundamental point of "jew i, odcopted, the prVtc/ple i. uni,'enOl. A more appropria\< parodi"" for lCCurin. cooSI"""'t conditioIU would be an arrang""""'1 wh.... by the .ubject (in the c.ampln. 1M .. a human bein~ tall be kept ...lrking ";thin h" Illdividually dcl .... min«l aDd iDdi_ oldua~nieaUy aI .. red O~flng rtgkHt . The c:cipJe, Iakt the lite "ry prtClulions binudf, i.e. he might adju" !.he rale and form 0( lIimuiltion 10 thaI • respo_ c:rilm.:.o, iJ>dicative 0( continuing laSt petiormana:, .. Atis&d; for eumple, by making lif. more difficull ifan indel or cotTed. pttformance inironmenl which fllnlisllct more than c"""gII _itly 10 ovenn tlu: ..,bjtct al any point in tlu: c:poscd method is as follows. 11U1Ud of Ih. dassica.l organi lm! en,itonmenl system in Fig. 57. colUnoo;( the system of Fig. S8 in ",hjeh th. conlroll.... iii a mechaniral or comp.net programmed. device for ex=!ing a steady <1.ale or null poinl operation, If p I, a performance index and if a ]C\·.I of tasl: diffieulty il rept eseft ted by '1 then the conlfoller in question dctcrminn li>c value of p, compares il with a n~lI poin l \'alue! (indicali,. of saHHactory and OOrrtCI task perfonnanoe) and op<1"al" upon 'I. as follows. for c:
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TM Cy/Jcn"/u 0/ Hunwo u..rnlng QN} hrf~ Iys~m i. ly:opul>Ov4lable if th. trajoctwy ~IWIlIy approaebn the origin and if it .-....er crosses from the intide In tru: ""u.idc nf a bn\&hCluy_ In sayi"llthal'ystt"'" IlK empirically stlble. I mtan thaI their irTeJllluiLios ..ilify Ihis OOI1dilino. no l\'t'~, and lILly be OOR$ItUClcd 10 do 1(1, In aU particulars. by 1M choice olapprop,iale functi nlU. The propnocd metItnd caD. be elaborated I peat dell. The alpilhm is utrem.ely primiti~, for enmple, and i. ~Iy impro''t'd thnus)! (u • matter nffact) ""'" imprn~ menlS ba,'e little pl1lct;a,1 ,"lIue, Th. conunl\cr dtSCl'ibcd abo". is unjdimclUinnal. ntis mui<:tion is inOSlef\lial. The majnrily of SteadY·ltlte conuoUe.. axe aotwly mul!ldhmnsional devi~ sn that p - (p, .. ... p~) and ~ _ <'1 " __ .. ~~). The perl'OrP1ancc criterinn is w:ry rigid. That cOlUtraint is ~f1ed in at least one af the •• ample. to be di.cusscd . The crucial and nutslinding luue' .... ta dn ""ith some half concealed undetlying .... umptions. Apan from the previously voi«d disqu.iet a~r the .tllul of 'ph' and 'pL directedn ...· it is t'o'idcnt that ~ controlln caD. nnly be designed to timplify. w.k (for example) if there i • • model for the w.k and fOT the rontrollfd lubject. Mo _ _, tty adequate mnctel for the w.k must be I ...pmentllion of tbe w.k as it is seen by the coatroUfd subject (ntherwlsc Ihet't' is It(>....,.,o to IUppose that an aUegtdly simplifying open.tion Muld ba,'t' the desired comequeDm)_ It is possible 10 numtTOll< e.umples in ... hich inl uili~ly plausible model. incorpon.1Illy, i.e. by a boot-strapping p,ocess.. f oo- the inuanccs 10 be cited, the booHtrllpPing works.

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The subject i. presented with. IXImpensatary diopl&y, usually no I r;albode rayoocilloocopc. In the one-dimoruiorW r;aot 1hown in Fig. 61 he perui .." the locus of a point on aline and isl't'
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The "e.t part of the control operat,on selects the eI ... of events from which one e,'ent will be 'randomly' .. mplod at 1 _ 1.. if some test trial i. IllAde on lhi. <>COII"on , The selettion probability for lb. cia" X, is denolod ",: and the conlroller of Fig. 66 i. designed so that

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The subject is presented with. the display and r..po"",,, board shown in Fig. 67. Each trial, 1:., apart, he is presented wilh. figtue in Ih. alphabelic display and requir«l to seleot the rOW and coltullll buUolU lhal designate Ihe row and columJI coordinates of the figure in the 3 x 4 rectangular di.play befort ~, seconds af\e, Ih. stimulus. With ~, sel at 2'5 seconds. tu al S second., and the between-tria] inlerval al 1·5 second. Ihi. is a difficult job, and Ihe no,itt is unabl. to do it unl .., he i. provided with cueing inforlllAtion. The &kill i, characlerised by a couple of error factors (in the sense of Harlow. 1959), namely, a row and column error [aotor, si nce the .ubjecf. response may be row...",....,t "od coIumn-cofToct indeJ"'ndently. He.lC<, Ihe cueing information i. de~,·ered with rtfertnee to Ihe row-response sr:1CC1ion and the column_rt'ponse selection separately, Th. information concerned i. provided by the row lam?" and Ib. ,oolumn lamp. of Fig. 61 which are illuminated al a vlU"iable interval (within the allowed iOlen'a] of M second.) after thup!",""'n,. of .stimulus fi gtue in Ihe alphabetic display.

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Finally each of U.e term, R(t,) and ",(n) i. interpreted as a bias applied 10 a probabilistic .. lection device (a variable 'window width' random nddr." ~neralor). Th. e!feet of equation (1) i. 10 inerea .. the test trial rate a. the .ubje,f. ,igilance decreases. and the e!focl of equation (2) i. to uhtar.." most frequently, Ihe most negleeted ..",nlS. The lall'" prIX''' maintairul tho a"era~ ".10<'$ of lhe ",(n) do .. 10 11m n.I required in the definition of vigilance. As a lheorttical aside, il i, worth com menti ng that th • recur."'" dell oi tion embedded in the design i, Iypical of ..I..i"islic system •. Here, vigilance;. defined on the ossumption that Ihe ",(n) art ~arly equal. There i. a rule (namely a psychological principle of familiari ..lion due 10 rtJ"'tition) which, if va~d, juslifies the I.. t control oJ"'ralion as an ',pedient for serurlng equalily of tbe "',(n). Since tbe rule i. ps~hologica1, the entire operalion is a Muristic recursion.

,• , ,

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+ I, if ,be i,h tJlp< ....1"''''. select.," i, comoct and P.....Oted) 1><10'" lbe ith typo cueiog information;

(O. iflbe I'h Iype selection i. correct but too lale;

_ I, iflhe j'h typ< response oelectloo ;. m"tak~" Or aboen'

Th. value of + I in this role may, wilh advantage, be replaced by the term 1:.1 _ latenoy. Define~ , as lite proportion of tJ.t Ih.l elapse. before the 'lh Iype of cueing infannalion i, delivered to the subject. The maximum value of~, is M and if~, _ '1_ . run no cueing information ofthe jIb type i, delivered. The control mechanism for variable delay cuei ng sali$li.. ~,

.. CMltllnt x Time Integral (" -

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4. 1 C10JUping T.chnlq....

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fw>cIa; t. $lead)'" sweailorion;". dil!icultyi
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o ther more complex lrrangemenlJ (described in the followi", ~ionl) were programmed on a $pccial'p~rpose computer (plate S) a ..... U u lM:inl built into numerous experimental or indu,mally u!ied equipment! (Plale, 6 and 7).

2.1

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Members ()f eadt. ctalolilte sampkd «juiprob>.bly, but each dus of ~ rajeo tory may be prtltRled with highcr or 1o_"C1 int.nsity (th. lower the inlmSity for the: Ith etau, the peate< il The lraince " required to inlerccpl l ho: wgt"t respooslble for. Irap-tOlY by u"'" ..... or, if need be, bolh or cwo ... mit:a! inten:epton lhal move up the righl_1wId lide of Ih. display. H. il ",,.,,,..j if a w&<' may be in l be offi~ but ;. ",,/ told which cia" of trajectory will charactC1iae ill motion. Thi. info"""'tion, which i, ..... ntla.l in om", to intemopt the target at all and whi~h mUSI he r_i"cd u carly "" possible 10 achi ..... a provident intcrccption, i, g... nered from observing Ih. first phase of a trajectory and combining lhe clues so obla;n",J with background Irnowl.dge loool tlol pos.
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ounces to QbWn an index of "",,«1 Mli<-f (Chaptef I), The rwity or Ill. rck'"UICC of Ill" ..,If-organi5&tion i. prutecd by any sd>e:me that ~nd.cn any dccreaoe in H, .... hich i. ufOll as. (VJtItrqlo;,,,,,r by IlIe ... gulator, COfI_ tingwt upon .itk' all inc:reuc: in ClllTeCt belief or a «Infl.ncy of «Ifl"f(t

""". 10 pr3£fi<>:,

9 Descriptions of Processes

schemes. of thi' tind W(lrt. wry effKti\'dy. ThcJ have a much

wicItt field of tutorial application dian IlIe do"",in of stntaured ,kiIb discussed up to this point.

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A desaiP'ion. of any .on. entaib a in .. hiclt the ~iption is t:tpreMCd and .. hieh can be interprtted by OOIl\tOIk' or IOIDtanding diltinction bctwten • slIItie description and the dncripl;on of a process lies in lIIe caplbillt;., lS$umed 10 ... il t in a uSCr (reeall. from Chapler I, lhat lIIere i. only pol~nliol information in a ducription, i.e . Iilenlty it ho.< • paue/n, it does nOI hau an information). BOl h SLa Iie paLlern. and pr<'ce..,,. may represenl du$CI ordered by the writing and connection rul~ of a language or fUnClion u nd ... lll iol1l. For eumple. a lable specm~ a ...lation and abstract automala may be rcprftented by l l1>ble (for in· stan(:t!, Ru of section 1.2 in Chapter 2). BUI if . paLlern il depicted thon the processor that uses it muSl be equipped with an otd", of e~ .....tion or I specially ope/aled dock (a tcelciOgfo~t progtUl) that rtcOnnitutH the table in ilS 0"'" otorage and refm to it. If I proom is repre5Cnted (Ihe specification RJJI incontraOito lhe , peclficalion Ru. fore.umple), thClt of operation i. eaTTil:d as part o[tbe pattern; il prescribes !be pcoceu to be ...."..ted directly and it may prescribe or permit many uro.otion orde~

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de"oid of conllict, h... an e~
II"tt ",thor lhan an execution rhajn. Several tokens oonld be moved down Ih.

I,," to ,ep=1 aim\l!\.lIIeO
n.scri&l pr",,",,;' thai a "'bjnneth.. impmtlh.. rommand may lead 10 III/venJ ""uJu (llOOied ax di'til\Cl. ho".. ver, unless there II II directi,'. 10 rool...,. Ihcm in a specific way). Wb.rCll" in .. rial .xecution, Ib~ command! are nea'Soar, Iy ... ",Ived .1 one value by a mctali ngu iSl,e ranking or maxi mum finding operation (Sh imu!,. 197J; Zadeh, 197J) or to yield one altCt"n.olive (by a biassood random oclcctioD). Non-dctcrmlni$tic PfOlI'"aIIlIIlOS (in the sc'"'" of Manna, 1970) ..... preocriptions of tbis typt. So arc the fuzzy Il80fithms of Zadeh (1973). If ..CCIlled by a serial de~, tbe condilional, lead 10 a nn,.,.."icaJ scMion a.i!'"illy'ng grad~ of membership in a fuzzy ..t; whore." if executed in parallellhe fuUJ' membctl oflh. fuzzy "I, or ii' .xtremum. form a nOn· num
More inl.ratiog poWbilitics appear if. lui!.able nr:>n·sc.iaJ prescription i. addrcued 10 III ex=>live 1gent having III/l-·e~ loci of control thai arc not n=...,ily independ.nt. Th<'SC loci .... mosl convenienlly ... gardcd .0 di'linci bUI inilially alyn<:lu'onou$ pr<>e:eUOtI tbal can be dlll"'n inlO .ynchronisation in sc far u the e:01 syachrono .... Ot alway> ••1"'. 0( the ... tire I)"Ilem. M...... 0'''''', the cooperative and iynchrollisins inleraction!l bet_a loci of control amOllnt to (non·trivial} inform.tion trtnsfCt". SubjWlcth·e i.mpcn.tive commando, in particular, s ive ri .. to this type of inl.....u:t;on (the simul· taneous exoeution of fuzzy conditionals. wb.re lite fUlZ)'sclution from one control locus i, lite inpul 10 • computation at lItOllter IOC\U). Let 1lI call tho prt>O!II obuined by eJ:li>C\lting thi. Iype of DOD· ..rial prescription a ~I process. IS ....... tho CQC for machine p
J Some Dd"m. ~OnCe$l d'scriptio", aU ~ve ~no.in defects (10 be discussed in a further volume) as they arc tailOred to luil vcry different appUcationl. Combinatonie n"tworn (BarralI.Torrijos and Chiarv;glio, 1971; OUarviglio, Poore and Bamlt·Torrijol, 1971) derived from I oombi\lalor logic approach 10 computation, repramt both ~!CI, lICrial and conamml processes. Petri IICU (Prtri, 19M; Holt. (968) ve 1lightly IDOre ~ncraI but corrcspondin&!Y intractable. Die..., (1972) hu discuS1ed the mAt\C1". One con~a1ed (some lay 'obvioul") u.umption underli" aU of those pre~rip1ionl and processes. Whether serial, por~lItl, or amrvr' nll, lb. procc", has a ~imr/Jr!l and an ~nd; at these poinl1 any proowor does ha"e a well ddIned 4tQtt. PenonaUy, I do not 6nd ;t II III ObviOIlS thai all p!"OCC$ICS do have bcgiMi"" IJId .nd... I'rocaf. COItld be ddiIIed •• """"llhi. property, or course, but m:my applications of lbe term 'procas· to rW activitie!l would be prohibited as • result orouch a ddinilion. r shall try to JUitify this poinl .... ,,~Il al illumating the other distinction. by ,.r.... 1100 to cxccutive agents less restricted Ibln most general purpose oomputen; namely, human beings wbo compule .,..;th oomplex. and variabl.·O
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by a marker to indicate its integrity and named or labelltd). Such a chan is shown in Fig. 87 and it can be employtd practically tlSing instrument< for a=$$ins and assigning parnmeter, to tepl'e$tntatioru of the subroutines. Plate 8 .hol>'$ One of them.

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what. Whereas ih e addresste or user may be e'pected 10 compare numbt'rJ. doe, he have Ihe ability to recogni ... more obt'u';ve prop«rie&; either abstraet properties like jimUar/ry or ""ncreto propenies like shape and colour that arc u... d in many ordering ",heme,~ The dilemma i, u,,,,,lIy r=l,ed (or "mply inchtd around) by appeal to 'we ll learntd ,!:ill". The solulion is legitimate enough if training in these , kill. i, pro,idor! before the user is asked to inttrprct the chart; failing Ihat, be is alm"" bound to interpret any command to do (not just the command associated with the decision table) as a command to learn. IrS(), the interpretation of the entire chan bocome'equivocal; variousoperationscoalesee into 'more or Ie .. wen [(amor! skill" and the chan bocomcs .-irtualty meaningless (it might as well be represented as a big deci,ion table). Suppose, for one reason or anolhe" lhat a proces& i. ",rially e.<ecu .. d. II is th~, possible to T.p~t it as a flow-chart. The ch~rt may nOI only be complox but repetitive. like any other serial programme, it usually contain, pam (i .e. subroutines) tIlat "'present the same kind of computalion carritd OUt in diffe",nl contex .. Or with d ifferent data. A ',ubrontine charI' i< a representation of this .tructure. It h"" elements 'hat may be either , imple conditional commands or subroutine. made up from many; Ihe only

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programmer hal pm:Iirud , miglll ha\'C bren made . This set omairuy con_ tains the corrtCt responsoe, aul il may abo contaio ""po= possibilities ... hich, if they an: solcctcd, indicale the uisccn« of misconttptiotlS about Ihe JJl3,erial in frame I. S. As in "'" linear "",", ,lit: .,..ehi... preocnls "'" "adent wi,h thc cot=\ response 10 trial nutnbcr N (Fra"'" I). 6. The machi"" usct, bu ilt·in dmaion role 10 dctmnine whieh f, ame (A or B in Fig. 90(6» ohould be: d i.pLaj'N alni&! n + J. The inpul o fl bis -e. 7. The studenl iJ asked 10 ~ontemplale tile correct respo".. information and (if n= ......y) to us< it in mOO ifying hi, com'epl ofthe maleri&! in fram= I (trial 0), When he II.., consid.~ the matte, , uffidently, Ihe otude nt indi a te' thai he is re:sdy \oJ reeei,.e the next frame (by p,"";oga button, or in aome comparable fru;hion). 8. The m. chine soi«u lhe 1le~1 fr;1me A or B, depending upon the evalu.ation of(3) and the decision rule 01"(6) and prnonts illo II>e lIu.:knl, Ocarly, "oil' 4, 6.l1ld 8 mediate utttnal fcedhitc k-rontrol based upon an e.,.aI.... Uon function and I decision rule that are chOW! by the programmer, Steps 3 a nd 6 rnedi.lte lbe: internal concaj'-e fcedbKk which i. present oven in a linear ')'Item. I( tile re" ... the evaluation and the dcci&inn to Ibe stl.Ldent. i.•. the SCuMnt is &iven aert.ain JIll .. (saying !>ow to woigll up hi. conslrUCled response: ..,Iali,'e 10 tile «,m:CC J'<Sponsoe) I nd o:t\ain dirocti,... (if you f«olthat your eval ....tio~ is 0, go to A. if b, go 10 B). The lIudont hi",""lf ..""" t~ ..... frftm • . Tho important point it Ih-'l • ,ubl)'Stem of the Itwicnl ha$ bren i..,lated as. supervisor and oontrollor o f his own education. using t he rules a nd di reeli ~es that are gi,'en . Thil may o r may not be a good thing to do depending upon the studenl and lb •• ubjec:t mailer. The t:lpedient certainly does impose a reiLI cogniti''e bunle~. Several different SOI'tI of programme network may be appropriate according 10 the intention behind the decision rules. The ca~ j1Ultxlnsidcrcd in Fig. 90 (6) is a network structure containing' mainscream linear ~"'" ..it!> remedial loops.. In the simpbl possible cotlditionl the response to frame / il en!uated u righl or wr~ and a decision is "",de 10 solect A (for pres
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misconceptiont IlI'C ""I righl. If the evaluation IJIIl the decision rules are more elaborate, "'" remedial action can be mO", di~mi ... ti,,& and ,he programme l iruceure may ...ith advarti.l.tl". be mon: &t.ailed, For uamplo, in Fig. 90(~) the", IlI'C t...'O diff=1 SQIU of ",toedilllioop (B. B" B. and C, C" C,.) 0"" of"'hicb i. se:1«1ed whm the ... bjea is ' ''roog' al frame I ; dich OM is .. lectl:d okpend. upon how he is lOITO!I8. The U$C ofremodial loops is akin to. ruei"! procedure t:lleOOed over sew:ral frames. lIccause it i.exteooed. it can be a controlled eII.ins procedure. The evalu.ation and do:<:i.ion proa: .. can also be u.cd as a mental testing facility to determine ... hat J,Ort of individual eaclt student i1. lad 10 prescribe essentiatty diffC!onl form l o f instruCCion fOf different J,Om of indiyid~QJ, A typicol progranlme network i.shown in Fig. 9O(dj, where Ihe ft,.n pan i1 a test seque"". for ',ming studenl$ into .Iassn and tbe remainder .. roe 10 administer .. v~.1 mo.., or lUI linearly arranged coune< contingent upon cluJ membe:r ship. 11 is usual (as ;0 tltis network) 10 pro'ide melt faciUti .. for reassigN"g Ilt""",,t from time to time. In section J ,.'. prtS<'flI & lutori.l conlrol p"""'" founded on lhe tkip ~near-programme net work of Fig. 9Il(e). II is a series of linear pr0grammes in whicb each Olle is addresoed to tbe inatlcation of one contept. From lime to time, l ies! of _ p t ItlUtory i> made and, if lbe CODCIOpt has been ma5lered, the $Iudtnl is dirocted 10 st:ip 0'''' the ..,majning framel dealing with Ihil conctpt. lIena: lbe: name 'skip linear'. TIle first branohing prOVllffifrln were written by Crowder (1960) w/so abo designed t he tin t teaching machines to administtt Ihom. ~bny people have .u~qlKntly been • • tive in this field: Galanter (1939), l umsdaine (1963), and Stohlurow (1% 1). 10 menlion only a fow of Ihem . On. special !,,"ogramming to:<:hnique is 2.3 Structural Commualo.tloJt t he structural commun ieallon methOO of Hodge""n and aennet (1%7) and Hoog.... n (1968). Any Itudy unit (correspondi"! roughly 10 a programme se:gmcnl) consi'ts of tho following section,:

"" ....

1. A statement o f the author', intention. Wt is, the uoottlying topic

~. A ';""po;"t ...·bioh onoOli the st!ldem and leads bim to t:lplore tilt: tiekl. 1. A prnctllalion of tbe: boekIJound ",I ...,.nt to Ibe COfICOpt of the study unil. 4. An iOvtSligation in which the student is po!oCI! probleom ....y &ve of them. 5. A w lution phase inyolving a r05po"" indicalor. This is a page con· taining ("y twenty) stalementS. all of which ",fer to J,Ome of tho problems,

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Tk Cybern" 6. A di5C\lmon guide. Conlin&enl upon lbc fludenf ...loctiq and not 50lecting certain combillAlion. of,late_nlS in tile mopome indiClllor; lie i. dirtcted, through. nwnw of $Ugn of anal"''' to ltlidy some: of the 'di5Cll5Si
2.4 rn.cn•..,. Lew", Slr"",l"r.1 oomn1unication is • procedural .eification of a doctrine c.lIed 'discovery lu,nin,' Or C,ince undiluled disco,'ery appears 10 be a preny haph.urd aClivity) 'guided \lisco,'ery' and i. a com~omis( belween frec rein .nd the aUlhor ilarian approach. Th~ b.,ic idea is ex .. lIenl. Moreover. il is empiriclolly suppomble, Le.rning takes place if and only if the studenl is impell~d to discover a coDnoction bel..... n already learned eOnCepti o. 10 corutlruct a ooncept tli<: point o f ric ... il is hard 1000...:lone AOasUUDption lhal 'd;'",;n-eoi is a pmpm)' of lbe mind "ithoul de1vins into lhe .ystems involved. This acid ""lieI .... is IpUf1ed on by • rul baard. Th .... i. no doubt lhal the ""'I"ili..., opc11lCiOll' ..lied 'disog,"efJ" .... '"efJ' important

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PrD«lm QN/ Prucrlp'/{)II.f fl>l' Aclion am/ u",ning and thai Ihey are much more diffleult to c:omprehertd than 'ad'J>la~on' (induced by beh"'iour "'. piftg). The majorily of writinp on th •• ub.fect of discovery are inrendM lO ease the dimClllly, SO Ihal discovery is liclionally oompreberutible as a popular lagword. In lbe proceu, 'di5CO\'ery' i. used 10 I1aJlle • scholastic laulol~ (a rose lmells Po= beau", ilhas ....-eetness; a mind disco,,,,, beau", it has lhe di .... ' .. .,. faculty) as a result of which the word faUsinto di,repute and the exce!lentw_pts. which aetualJy underpin the di..:o'"efJ' doc1riM. fal1"";th it.

2.5 Bchorleunl Objt<1l_ Durin,lhe last decadeor 50 OIle """",menl (abo>.. all otbe1"l perhaps) has had. Alul"'J inlluence in leading pcopleto think clearly aboul lrainin; and edOKati"" . The underl";ns dosma i. 'behavioural oI>.fectr.~' (Gagne. 19(2). A•• tone and iMII/licienl ~ the dogma ""Ids, .. folio ..... (a) 'ThaI the terminal mlm. of uaini,,& and leaching Cln 1>0 c.'prc:ued in 1trIIl! of behavioun (onu very comfllex ones; for Vlample 'IO~Uiply numbers A to B uoinS a .Ude rule' or 'multiply numbers A to Buling I lable of log:uilhms' or 'mulliply numbon ,oj to C'). It lbe .. behaviours are co,... reelly performed a Sludenl ·kno .... · ... bal",'", (multiplication, fo< .... mple) i. required of him . The ... ord ·kno....• is placed in inverled commQ beawc of a rontenlion Ih~llhc piny of behaviours is all that an instructor tan know (wilhoul in,'ened 00"'""") aboul the stud.nt. (b) The romplex terminal behavioun can be broken into ,.gmentl and Ihe oorrtCt perform1Ulce of these smaller pi=sofbehaviour. usually induced bybehaviour Ihapi ng. i, a sufficient ent'y crileria for. behaviour shaping operation that inrul""los Ihe terminal behaviour (obviou!Jy ra) and (b) can be iterated ... ilh ..speet to e!lC'h behaviou!al sellment unlil ,'ery . mall piecu of behaviour "main a, primitives and, in principle, unlHlhere il no rf/!.idu.). The ...hol. gamut of method, and models ("";tb Ihe pouible e~~plion of structural communication) Are pgpu lady adumbrated under the rubric, ' behavioural ob.fectivos·. Training programm .. lire .erlainly devised On thai assumption and olkn more or kss work (though how elfectil.. ly il il hArd to 1011). The plain fact i.. ho"""'.1f di"",,'ery .. taken !triou.ly then neither Ibe contention of (al 'ccrminal behaviOWl .... all ~'e CIa kIlo ... • nor the conlention of (b) 'il i. pciSible 10 .. gmenl any $kill' hold 1VI1(f. If di"",,·ery does JIIQJ\ a cognili", ",~nl IhCfl ..... "... and "'.... / know. in order 10 RIppon thl. vi ....·• how . i1udenlromprebcnd, a lUbject mailer. deacribes it, and explains il. True. lbe dala may oome from objecti..., ~ of ...1t&t !he $Iud.nl d .... bull/tcy ""' OOIlnlerpreled Q beha"ioural record .. For uarnpie, pby.ically a...:l operalioot.aJJy t!lm i. a year dcal of dilferenoe bet.......n 'multiplying' aod 'uplainin, multiplication' lboup il may be !he dtl for lbe

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11

Learning Strategies, Teaching Strategies, Matching and Mismatching

Le,uning depend. upon Ihe slmt.si •• usod by utudem io ordet 10 dir«t hi, au.otion IUId to partition Ihe educational goal imo .. parat.... bgoall. At OM extrtme, Ih""" .!talegin may stem ftom Ih. stUdenl him$Olf; they ate letlfw;nl fIrm'lie. which he briop 10 bear upon an OI:h ..... i$O ulUlruClured situation. AI the OI:her .xuecrcu the tlecutioo of ather Wlt.yes rests upon a '...-iaI.i'ol' compel.""". By bYPOlbnil, dfe<1i'1' kUIlipg t.ab$ place ir. aPd ooly if. lhe individually.K1ec:tcd (learning or ,,,"chin!> wateg" I. matched la the stlldenl's t:Wti"l compelence. Su>d.OIS ar. ~J\naUy una"""" of tlteir compelence, and a f...., learning srudmt isllllliUty 10 !earp ...~U. The combinalorial problom of matinl the ....... tegy 10 a (~y UnlwlWll) compel.""" profil. il coru.idm.bIe 011 its cwo, bu, lhe!·. are also sptciDc facto .....·hiohmilital. against effCCli,-e "arnill8 by positivtly .nc;ouraling nmm.o.ICt. On. oflbe mOIl importanl is 'cognitive !lxili. a I.ndency 10 &dh.re 10 an originally $OlCCled Iltotegy .... n in Ih. face of .videnc. shOwing il to be inapproprial •. Th. po,ilion i.lOm..what ditT.~nl if a I.ach.r or a t.aching prapmme

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3.1 R.Llu.- ..... TypesolStnUetY If a relation It is dacribed in lbe conle':! of its donWll, wn It has an apparent dImension, n, eq....:J to the nWllber of properties in (dacriptors 01) ill domain and In onIer or .,:licit)' m equal to the numbe, of pe tmlU ~111 d imens.ion and order .... easily intcrprelllblc (in lbe casc tbat R is nated eAtt:.MiotWi), as • ",Met of the prodllCl of ' ..... bIes (U.) irtdtxine: therelated ~ies). i.e. u R l!! U, )(.,., X U. _ U" ... hen u ... tuple ( .. I, _ ., .... ) e R l!! U" wi
all,,,,,,,,,t : (a) if n > m (as tIlual), then R il tbe interseetion of IIlbrel.tioM (cylinder ... \>$(:15) of generally 10.... ' order and di ..... nsion; (b) lbete will ofltn be se"o'tn.l families o f 'cylinder lubstll· Ibal inl'" sect on II ; anyone family lpecifies R; the set of familiel p' or 'til<: T.e.A. c)'tle' or 'A allow. B to do C' o. °happ;ness' Or 'an(¢lopc' (a clas. of animal, d.fined by rdations betwnn belUlVioural or phylical properties; the laxonomies we actuIUy .mploytd classified mylhical, Martian, crealures .ince the'" were necessarily unfamiliar 10 the subj(C!$). Sometimes lhe orMr of til<: ",lalion and the dimension of il. don... in are c~plicit; for instalKe '>' has. ord.r 2 and is irredundantly specified (f~. num.rical domains of dimension 2: similarly, 'A alioWi B to do C' has orde. 1, Ihough Ihe dimension is not .,plicil), BUI, Hne:uis1icallY'laled ,.lations can be quilo re'pedably under_specified. II is pouible 10 lisl !.ilualions tIlat cllFnder happines, or ",lations supporling the antdope dWllC1er oJ l'!finirorm. "The", is Mthing my't.rious aboul the idea of U\ undcrspeciflcd relation. OD!he other hand il;S "" importanl and interesting idea. An individual who undemands the language in "hich the relltion is 'Llle
uarnlng SI,aug/u. r,achlng SI,alogloz, Malch/llg a..,J MUlllalching union of fully !lpu!he tint type ofproblem $OI\"fr'" a ma~mbltr ,Old t he KCOIld as. dire<1o.- and. compiler combined. If .... make lbe oaJDII distinction in (¢tuIS of artiDcial intellige= and psychology, "''C can say tIIIt lbe tinl..,rt of problem ..,lving resembles Ihe operation ofa ptOg:rammc .... h &I N......U. Shaw and Simon's 'logic theorist", w~.... the second _t of ptobkm soh ill! resem.bl .. the op.=tion of an MIOciati.t IItlwork like Qujllian's(I969) 'TLC, Wlten R i, redundantly specified (as it is) lben the second sort of problem IOh"fr alms fo ........ru sllbgo.als at 011« ~ i, likely to lchie>-e R Illbe inlcnection of various families of Illbrelations. The crueial pcint and the reason for making this di.tinction, rather than many others, is lbat (in common with lOme other paiR of procuse.) tb ... two are i ncom pa lible. Data used by one p.ecess can not be UJC
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TM Cy!>tm./ir:3 af H _ iAIJr"["I IfItd PtrfD",umu stillod .x.a;ptiOll Df knowledp. To""ow .lUs poinl., comider any Ilescriplion of an enwlm .... mtlb. Amonp. olber dDcrip'fln, il is poKibl. 10 ~ (and '0 oblain 1M promised .. nse Df ... opi< ,t1abOfl wIIidI is '.htad Df' another, il is necao&ry '0 cI>oose).' \east om: descriptor wi.b the broad COROOlalion Df ... bordma~fsupttordi ~. In ........ of ,Ais description lhe Iopic: ldalio,," are partially ordcml; is,oneupeaoflhrirdeocriplionis panially ord..-.d and q~il. possibly tlUs ()tiIHinK 100" Ute fi&. 904. within this ord.ring, some IOpiC relatiOlU are 'ahead or otho .. and, U I rule, lho loal relation is pl~ ., the top au 'head' in .his de1Cliption. The! ....... ial point i,that Ih.re.re many desrnpliom wi,h dilferent 'heads' for Ih. same entailmen, mesh. In faCI, Fig. 94 i, such an ordering and it It,ll one intrigwng ehllfacteristic; namely, Il~y lopic could be chosen as head in .ome dc .... iplion of'he IIndorlying meoh. Thai is. il wonld be reasonabl. 10 learn aboullnnh labl .. in tH'ns of .ariabl.. and connecti'·"(as in fig. 94) Dr. \lSing a dilf.rent ord.,ing, 10 tum abou\ ronl..:"'i ..... in ~rJJ1$ of mnlt labl.., .,.. oariablos in tmnJ of connecti... and .nlll! ,,,,lues. The sororod mjuiremcnl (a moans of dciectins !he undmtaQdinp IMI SO Dn in aconvenation) is bcllraclded in thecoru.exl Df an.ruai..... nl rnnlt lhal forms the: convenational domain; Iho 10pic or subje<"t malic, lhal is under di.....>Ioion. In this ODfIlU' ..... need .. mechanisabl. ,.., for IInder" $!aDding. The 'mect!onic:&l' ffClui"' .... nl upon lhe .«1. 0' de.eetion de-oioe is chiefty imJ"""'l IO ...sure Ibat il i. ",... 11 ddno:ns upon whi<1! llroder. standing is reached by II p'rxm, wilhout 100 much commiunent aboll. dn~ the process it ex..:u.ed (for .u.mp~, in the IeaCher's brain, in the srudcn.', brain, or in some ,nanima", processor). Thi< proem. mighl be doemed 'nl.lligeru. (iA. an insWl« of intcllcet and not i\1S1 'able 10 past intelli&
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5 TantlJlg Wild UnUnllndi"l: The mclll.o. •• undeTstanding in a CET exletnalisod ron'-ersation is sho ..l1 in !'bIOS I I .00 12 (tbcsc pidure$ are chiefty inlcntkd 10 p,.••he reader an OVCfl'iew of Ihe cquipmcnillied in srudies of \earninl; IWI, in this volume, 10 inform in any dcplh). The .ystem i. founded ILpon a theory of whal IIndc,..taroding i. (puk. 5<0.1., and Kalli kourdi., 1973) and lbe followins «ImmeOrncntarily fOC\l$lld at a &i>'eo occuion, there is • ....hIe eotily

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1!"'S 5 ~ ~ e.. !!:;.<:t: 11 :; 11 loE 0< i(g!tEI~h;.B8 " g "5rj, ci""" ]~"~i;5 l ' •• ] t' •. .l!' .~ 10'; §: t~a .'3]<,.' ,

f..~~ ~.E "",,'"

;, !.~ <111 .

i!":4b~]

".E .<:~,,~

S~-l:.c~

; 1l l~~·i .!! .2·.. "

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-

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o

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TM Cy/Hrflt/j" 6/ }/~mtJn Lttrmlnt!mil Ptr/~

"'i", probab;li.y numbus lilal do ro/Ica his """'" 01 belief. S/lufOt'd., Masooncin &lid AlbM (19f;6) dori ... ,ho.-ry an.d , ufficioatrhuno:la and bas ,lie 1<1"",..", ""'" otllcr sudI sdlemeo tllal lbe S1udnli"s..,.,... dep«MIs only ott 1ho value I>< usl"" 10 ,I>< COITtCI all ..... ,I .... Gi>UI tht"."..., ......... I'rd""", ahemati... is tl>< jth allernall .. ODd !be usiped val ... 10 II>< Ilb alkmali>" is p" this """""'" lp
f.,...

Appendix C

i""

,wo

tllat:

,"0

_1".

(I) if P, is """alllan.,.. equal ,0 (1- 1, ho r=i .... I (2) if P. is less lhaa(l-l he tffIrila - I poinlJ_

+ iolP, pow.. an.d

CooditiOd (2) prOYiIks 0 CUI ofI'point tl>ot Ji ... " poiru..:ale ftlDDinSi'l'om -I to + I ( ... ther ,1Ian _ <0 to + I). n".. , rot ... tmne ........ of P"""",,, infcrml'iort illa!t. 1.0 any practical "!'Plica''''", th" Ioos in occu~ is i",i",iflCan'.

Fuu r Open ,lonl (Zl dtIt)

_de,

For a lhorotlgh lksl'e of mombcnhip, i.• . C/"- A .......tuny ..,~ oeI io 11,,-)( i....... lhe "";.,., (""';u.., UN. Zadolt ..... 1110 kl.1 to ....... poftd inlldinitely 10'1'" unions) of <ertain unl' sots. Tha, Is

_lie,

q"

""de.

'=r

..-

X ~ UN(C.(M)M The complrm<no of X Is

.., ..,

No, X i! W( I - q"lM The union of f~ ..y

"'I X. Y. is

Or (X. r ) ~ (.!ililX C.M P C,.(o-)J/M wl!ere 17 is lhI: maximal optt1lor;

'P ... M....

v..)~

(""'1 .if.>,

Tho iaIorxalott or fIaay .... X, r ..

.. ,

ad (X, y) ~ U,.'(C.(~) ~ C'(.)I/w

w""'" ...Ito ",inimal openlor ~

r ~'''M'''V'')~

'"

('"'' 'I

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G'-, Rdlllon II A ~latiot1, Ii ... n as • listin&, is a subset R <: S x T (for eumple, if R is 'married 10'. !ben R contains an thooe men and '"omen who are husband and wife). R IIUI)' also bo rep=ted b)'. QUIpping IX ICrie$ of liI!bgeo bet ........ the elemonlS of $ and T. In • monopmo ... soejoty R is. one 10 one mappinl' Qel>....lly. R may COIISi" il> any 0 .... O!le; 0 .... many; many, one; or lIWIy. many mappi"llIId il may inYOlve 011 Or only some of the elemenl$ (lbose involved .... caIkd R'I domDlIr and codtJmallr or ""'J:t). In go .....I, also R c: $, x , .. x S~ and" is ~.llcd th.adi~ityofthco ~Iati"" (thu, R c: S " T is a 2-adK: Or bi nary ~"'Iion).

Glossary

The items

~

arranged in an or
Sot S A collection of WIOfIIered unitary elements. M embcnlUp ill the colkctioo if; wri(1tf\ 'e' SO tM" e S means 'element J i... memlxr of oc, S',

Flm<1l... F A kind of relBlioD; c-ither • 0 ... 10 one o r many to ODe mapping with specified domain. If the domain i. Its. Ihan an (Understood) Sotl Ihe fUDelion i•• 'patli"l' funclion. Since Fi •• pecified .. a ro!alion F <: S, " ' .• " S,. If is the ldidly of Ih. f\l!lCtien (or. eq"'valenlly. F i, a rUDelion oh vatiJ.bl<'S).

Sol_ X • 'portion (If. ~'(""'il~n. X C SI 'either. porno.. or or allor,

Vlriule A nlmod indexing dc"ice lhal auumes bul one >1llue II~. For uample, a vari.\bk u ilIal range. """I' the .lements s of S;. varilble ~

a st1' (wril!tn. X I! S). If !he dc .... nll of subsets are specified e>:plicitly the clemen .. in 'l.lIeSIinn are .nclosed in bra
ilIal ratIF 0 ... ' lilt ~Ie""",u , of T. ~ valuos of u d.... ou .kmenlJ or S, lhe values of 0 denote tlemenlS of T; in ge.....t •• ....acr ( u, ... u.) of" >'Uiahlcs indeuM .1e..... nlS of S , x , ,. X S. arid ;IS valll.lilt-and for ,..tupla ( s" .. I.) e S , ,, ... X S •.

Pow.. Set 'The oc, or 111 lublets of. st1 (oawally, inc:1O>diog !he mJl or

F~iol\S ate oI'Ien tlassified by Ihtir domaill/l1IJIBO for exampl., 'Boolean Funroo ... • of a variable ... uming values {(I,l f (or 'True/FaI<e') and having possible values (O.I) ; an ;nttger.atilhmetK: fu""lion (of a variable with integ•• val ....). FllII
~mply

5<1). For uampk. if S has .kmeolS {",b,c} then lhe Po....... t of S is {al. {bl, Ie}, (",h). (",oJ. (b,c), (
illlcl'!CdioD, Union If X and Yar •• ub$ets of S then X n Y j. the In,e,.. stctitJn of X and Y(the sublet of.l.menU of Slhal beloog to X ami 10 y) whilst X u Y is the un/OIl of X with Y (th e lub\t;l of element. of S belonging ~It~r to X or 10 Y Of' b
""'po«

10 S 'T'he IXImplemenl of X is $ _ X; the

~Ic·

men" of S tbat (to 110\ beloA' 10 X. OIs}oJll! SoobstIs of S are liubseu. X, YeX co S, Y c: S) lUCh lbat X n Y isYOid.H~DCe, X ~ S _

rand

Y ~ S

.. X.

ProperI)' That whieh is commoD 10 the memben of ;0. Sot! ffo. eumplt. if $ .. the Sotl of lhinp, X of red llIinp, then X is the property 'nd1>C$$'). Cut ..iu Prod""l fn. two IX more 'eI$, S;tOO T. Ih
"> • m

Class.eJ of Ftmol\oftt

aa:ording 10 lhe number of v.riable. n..d. d 10 ;!\d.x their domain, Thul F(Il);. a I place fUllction. AsoerIQri< Lot:k: (In COntrail 10 command logics and quell;on lolies considered in tbe leXI). A language logetlw:r wilb rulH for usage (IYOW) and inference (see bolo"'). Slal."",nlS in lbe lan&uage an: si"'~ ..emanlK: interptelatiorut; eMllI'IOILly It denOlin, relatioM and rolldiliollS WI hold in 0Jle or mOR Sotll.

Propoo;Illaa p lin a IInIUIF) A Wlemeol liU " is red' or', II married to " atId inlerpreltd, if Itllt, ali 'S. X" or '(s.r>eRe S " r , "'"ital. P An adjeclive. Eqwlignificantly, !he name for I (usiWLy partial) fuDOtion from a set S to U e! of truth valu ... Commollly. 1110: lrutb ,...r"",,1 is UlU~ 10 be 11.(1) (indicali"ll 'true' and 'fw') but thil il nOI al"'lIyl \he elK (..e, for .umple. lhe Fuzzy .. ta in Appendi. C). If II ill variable indicating members. J . of a "I, S, then p(u) _ Tru" 11 a OM p!"et pr-e
.!!!.

,

j I !

'1M CyMrnellrJ of }/umon uarnitot anrl Perf"'mtlIIce M~Ira- MlmemlllcaJ I........ A graph i. a l!rucnU1: coolillizl& of Mdu (drum IS points) and C(lnnt<:,ing < Theory " i ll fiDeI L_ and Raiffa'. GI1IIVJ anJ ~1oIrl (W iley. 1951) $Iil1 the ...... , readable

References

and in/"ormali.., "'ference.

!\tl$ceD_ Statiltltal T ...... u.... I•• ~ n,.n_al '""'''' The following commen'" afe .uperf\ci.al but easily upnt... by reference to any elementary S!.Ii.Ii", tnt book. Th. nlNlt of a set 01 o~tiolll ;. thei r .,-crago (Iri lllfMu.: mean) ..... h>e. The i. an inde, of "",ncr about tile mean (u~ually the IItl11dDrrl dt!:;Q,ItNr. abbrcviat ... as SD is cited ; tru. quantily ;, the "'lUll.., rOOl of the VlrilllCC). A lignifict._ level (cited " , a probabilily Of I pefccnlOSC) i. attachod to lUIy serious COmmen, 0' finding ; tbe laual lllllucs'l( I r. I nd 0'] r. (or p'" 0-01 and p ... 0'001 ). Thus an assertion thaI a ny numerical qUlntity is lignitlcanl al the 0· 1r. level (or 0 ,001 ~ p) means thal Ih. quanlily mighl bve .... urn ... this ,'alue hr>phuardly or random ly " 'ith I ~ha_ in llXXJ Statislioall<$lS arc emplnyed in ".,in& hYPOl h~ aboul absolute va1\ICS. difJ~"'"O'J belween mun values. and IUtuh (for exam ple, 'the dilTer._ is significanl al the 0'1 r. le".I ·). CorrdarlOll codlide nu rtlCtuure the UIIdin:cted (olher lhlll random) . $$Odllio n belween quant;tic:I ; or>« again. correlation. ITe quoled l ogether wilh a properly calculll'" I.,-cl of

.,,,/tmrr

significaoce.

II

ACJ:OH, • • (I91) .Scioft<:e in d•••ystems If'. 01""'1_ Ri-.lo, MayIJ _ . 661 _11. ~ .. u .... n ... o. (I!t1Jj. RUIdom Jopo .... ; ...biliryand """ptlon. lit'. J.I. M_M«ltbtt SlIIdin.. 'II) ; I I ~J2. A" A• • L••. ( I9$). RcptesWiorI of problema and pl dil1Cltd protedura in computen.. Bulletin ASC I NO. 1. I-J,. A"GIL . I. S. and G. A. l u n (1!I68). Adoptl ... ftoi,. modeh 01 "",nual coa. trol.yst ...... I.E.E.E. r-.. ..... M_MII<JdM Splmt>. MIlI'dII968; 1!!-21. A,nl . .. . (1966). C~'kltllfd ~ Press.

Dttos.,-..,.

..... 1........ (196f). Brd/Pu. MlI
..... IY. w ••. ( 1968). Som.o COII$OC]""1I
1arJe')"temI. C............. ASC. I; 2. AJ HH. w. I . (1910). Informatica ftn ..~ wilhinco-otdlnalod pp. H-64 . I .. ; Pratrm DI0obn".,Iu. J. It_ ted). GordQII Ind Bro.och. ".,.,"'>lSO". ~. G. (1%9). MocIcII rOt """"Cry. In; ~ ~ h~ F. de Brioson.OO M. de Mom"""'iot (edI). Ounod. AUO N.O>l •• . C. ami . .... IM""'>I (19117). 11_"1"'''''': A ~ S)...."'.,J III CMIrflIl'rod«ilotr 10 ""---.I CI1IrM*J. Holt. RiDoIwt

IY"""'''

_Wi.....",. •. (1 969). T1te....cenaln ......... 1tId tho u........... DCliiet. New YD
"~" •

11_.

m

I

-

-J

I

•

.," J !

!

,

•, ,

<

.!!

,

;n~

~N

! , ... ""'~ -Ii ... - • '"

~

8 -!" ~, ~

""

D..'"

N

0

N

•

•

UP ,

~

~~.<>]

;;

N

•

<

N

• ••

~:i

",, ,I »

H ~ "5

~~

,u •

• ·r

i~ ~

t~

.5".8 «

~~

,

Index of Names

Bonner, J. T. 70 Boulanger. G. 11

Acl<<>If, R. IS Alben, G. 30, 312

Brommerman, H, J. oil!

Altksan.m.1. m Ama .. I, S. 28~ Angel. e. S, ,60 Apt." M . 67, r,g

llrider, P. D. 24 Brillouin. l . 41

Arbib. M, A. ~J A
B'<>adbent, O. E, 12 Brodey. W. 14 B",,,,,,. J. 260, 262, 26J Burb, A. W. 14. 60,

66,67 Bu.h, R. T. 'So 127

Cane, C. P.22' Carnap. R. Z8

Ila<:h, E. SS Sak
Bailey, C. E. G" HI! J!anerji. R. S. 213, 219. 233.28S

Banniot .... D. 1&2

c..nkdg<. J. W. 9B CU!ia.!, J. 244 Olionl';glio, L. 28, 66,

Bar-Hillel, Y . 28

Barioolll, M. 67

CommoIl<1". E. 230

Sarralt.Torrijot, J. 221 Barron, R. 1. Jll

Conant. R. 19

a..ttw", G. 99 &)'"'

30

.lOO

eo",,", J. D. Sl

Crai., K. 12 Cr"",ouo. E. R. F. W. ~

lieJ<ey. G. A. 200

Cr<>Wll
Seer, S. II. 82. lOS

Ilelbi .. R. M, 2A! Bell, G . L 78 II
Beurle. R.l. 111 Blum.

j.

63, III

EI.boot, M. 260 Elshoot, T. 260 E!;tob. M. 2J Emot, G. W. 156 Este., W. K . 127 Evan •• C. R. IS9

Feigenbo.um, E. A, 156

fold","., a. 156 fold"," •• R. J. 71,

n.

"

f ..tinger. L. 39. 265 f inelli. DruM Dc JO Fitts, P. M . 24

Fogel, L J. Fu, K. S. 213

n,

OlOmr.ky. N. Sl Codd, E. F. 67

Bat"",", C. 14, 232,

EImoghraby, S. E. 230

Davi~ I. K. 2S4 lli,;" M. S7, 58 Dexter, M, 158 0)", o$e o><.io, R, t>I4 Oienes, D . 221

albbo.y, O. M. 15

a.gno, R. M. 243, 247,

m

Gaines. D. R. 53, 169. 171,207,260 Gal.nle" E. R. SS, 127, 241 , 245.264 G_~

Gilbert. T. T. 23S. 237 Gilstrap, L O. III Glil.l
'"

Ghl.~kO", V. M. Il, 67 God,l, K. 58 Goguen, J . A. III Goodenow, J . 260, 262

Imkx of NdlM.

The Cprn
Grey Walter.

w.

'"

Guilford, 1. P. 263. 264 Hagen, Ii. R. 66 Harlow. H. F. 114 Harn.h, D. 22, 83. 216,

"'

Har'ley. J. 2S4 H.lson, H. S4 Herrmann. R. 11 H..... M. 90 H.wi". C. 21S Hk~. W, E. 24. 26 Hob ... L. C. 230 HOOg...,n.",.141.142 Holland. J G. (>6. 23S Holt. A. W. 6!l. 1l8, 220.221,2)0.232 Homme. L. E. 237.

:m.254

HOmlbiIJ. I. S. 22l Hol'oUd.N.300,301 H udson, E. M. 169 Hu"'.9. IS6, i l l Hyd.n. H. 09

]vanh.nko."'. G. 11.

m Jonckhee .... ",. R. 191 Kagan. J. 37, Z63 K.Hikourdi<, D. 96. 291. SOO Kauffman. S. A. 67 Kelley. C. R. 169, 171.

m Kelley,E.J.111 Kelly, G. A. l4. 182 Kerne.-. E. H. 78 Kilm .... W. L. 63. III

Kicene. B. C." KODonki. J. liS

LaiDg, R. D. 300

Lappa. U. 2lJ l<>e.A.R , 300

u'ichovsky, D. 61 t.-i$, B. N. 78, 118. 181.182,186.187, 194,207.225.226, 260, 268. 300 UUy, J . C. 189 Locfgren. L. 60. 216, 280,298 Lor""z., K. 100 Longu<,·Higgim. C. Jll lox:e, R. D. 55, 127 lutnsdaiDl!. A. A. 241 luria , A. R. 263 lyapu"ov, A. M. 165. ,~

McCulloch, W . S.Il. 54.6.3.82. Ill, 231,

m McGill. W. J. 20 MoKinnOD Wood. R. T.

'"'

Mallen, G . 147.202. 210 Manna, Z. 61, 190. 220 Mair. J. 132 Marin. J. IS6, i l l Marld<. S. M. 235 Markov. A. A. 219 Moson. P.43 M.... n&ill. H.lO.112 M.t"""'". 1. E. 127. 259 Me.ul, M. 11 M... rovic, M. D. III Michie, D. III Min.r. G. 55. 245. 264 Minslty. M. 54, 55, 57, 61.65. Ill. 156,220 Moo ... 61 Mosteller, F. t27 Myhill. J. 60 N.gel, E. 58 N... mann, 1. R. 58 ,~

N.... H, A. 156, 260. 2-85

Owe"., H. J. 147

Pappert. S. 6.3, 65. 220 P.. k. E. 23. 43 I'
!'
!U.pap<>r1, A. 9Il R .."e""y, N . 11 Reitman, W. R. 156.

,.

Reja., G. C, 98 R«clI<-r. N. IS. 21S

R«int1, S. 244 Richard 58

RQChlwso, R. C.

(>I,i

Robinson. M. 9$ R"""nb4tt. F. 63, 220 Ru ...n 58

SoaooUlO. J. M. 91 SclIneidmann 11 Scott, 8. C. E. 23, 96, 158. 159, 202, 207. 265.267,268,271. 276, 1112, 28l. 288. 291,300 Scigrnan. P. 28, m, 111

Shannon. C. E. 2!1 Sherwood, S. t2 Shiffrin, R. M. 1J8, 263 Shimura. M. 220 Shroedinger. E. 41 Shuford. E. M. lO. 3t Z Sime, M. J1t Simon, H. A. 63. 156, 260,285 S~inner, B. F. 160, 215 Smallwood, R. D . 127 Spencer-Brown. G. IS.

"'

Slan ;.tond. A. C. 21 Stapleton. W. 28 SlavriDides, A. 63 Steinbucb. K. Von 101 Ste...art, D. J. 45 Stohluf'O\'l. L. M. 241 Svoboda, A. 11 S""",. P. J. 156. 262 S",e'" J. A. 25

TOIIIl
Urquhar'. A. IS lIttley, A. M. 101 Van der Veldt, J. 195 Von Gich. J. P. 21 Vilal1yi. P. 67 Von Bcrtel.nII)'. l. 11 Veo Foerster. H. 11. 55,127,128,129,156. ~.~

Von Neumann, J. II, 53, 59,60 V"" Wright. G. H. tS

WaddingtoD, C. H. II,

W Wold. A. 164 W.I,h, M. J. 141 Wa""n, R. M. 139 Wott.nab<:. S. 127 W.., ..... W. E. 25 Wel ford. A. T . 12 Wieno<. No ll. 14 Wil~ in,. l. 6Il Winograd. T. 53, 100. 215.2n Win5ton. P. 100. 122.

'"

Witkin 263 WittgauleiIl, l . 83 WoOOwotth. R. S. 195 Wym'" EdI'oUdt, W. C. 91, 98 Zo

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