Machine Intelligence 7 - AITopics

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PROGRAM PROOF AND MANIPULATION We define the number of occurrences of a cell in a list by induction (5: Ux..T-4N (i) 6(v-,v)=0 (ii) 6,4(x-o a t/ x-02 w)=6,a(t1 x:-,w)+1 if x=u a =3„(t1 x-+w) if xOu It follows by an obvious induction that 6„(A • p)=3„(A)+6„(p). To keep track of the effects of assignments we now define a relation of distinctness between lists, that is, they have no cells in common. Distinct: 2' x 21-4T Distinct(A, 1t)
BURSTALL • j =RE VER S E(k) Assume rev: U*4 U* reverses strings. K is a constant string. ':=nil 1 K — -k-nil e Nonrep(k3ni1). a IC — --(343)[k->ni1e 2.j3nile 2. Nonrep (k-> nil). Nonrep (j-> nil). Distinct(k- a> nil,] -1-3>nil). rev (a)fl =rev (K)]. a YES rev(K) j --> nil e 2. := ilk (314)[k4t1 k e 11 k-; nil e 2. Anil e 2. Nonrep k-a>ni1). a Nonrep(j->ni1). Distinct(k-> ilk, ii k-3ni1). a P 1 Distinct (t1 k-> nil,)->ni1). Distinct (j->nil, k-> k). Unit (k411 k). rev (1413 =rev (K)]. 1 P °- -- — — (3143)[k-> tike 2. i;nil e 2. j-> nil e 2. NonrepOni1). P 1 a Nonrep (j--)ni1). Distinct (k-> ilk, i-)nil). a P P 1 Distinct (13 nil, j->ni1). Distinct (j->nil, k-> tl k). i Unit (k->t1 k). rev (a)113 =rev (K)]. ilk =j I a 1 P a 6- — — ---(314)[i->nil e 2. k->j e 2. p> nil e 2. Nonrep(i->n11). j:=k k:=i Nonrep (j-> nil). Distinct(k4j, i->nil). a Is P : Distinct(i3nil,j-)ni1). Distinct (j-nil, k-)j). : Unit (k--)j). rev (a)1,3 =rev (K)]. Figure 4. Reversing a list. 31
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Page 3: MACHINE INTELLIGENCE 7
Page 6 and 7: © 1972 Edinburgh University Press
Page 8 and 9: PREFACE the speed of calculation is
Page 10 and 11: PREFACE them on the shelves until t
Page 13 and 14: CONTENTS INTRODUCTION xiii PREHISTO
Page 15 and 16: INTRODUCTION Among the many propert
Page 17: PREHISTORY
Page 20 and 21: PREHISTORY discussion of the later
Page 22 and 23: PREHISTORY beginning to wane. I eve
Page 24 and 25: PREHISTORY I don't think that I can
Page 26 and 27: PREHISTORY discouraged by the slown
Page 28 and 29: PREHISTORY carried some fixed patte
Page 30 and 31: PREHISTORY After completing actuari
Page 32 and 33: PREHISTORY modified program cards,
Page 34 and 35: PREHISTORY REFERENCES Champemowne,
Page 36 and 37: PREHISTORY and they were joined in
Page 39 and 40: Some Techniques for Proving Correct
Page 41 and 42: BURSTALL (a, j)+ 1), treating array
Page 43 and 44: IIURSTALL a'(0> 0. The distinction
Page 45: BURSTALL that a is a list from u to
Page 49 and 50: BURSTALL j=REVERSE(k) Assume rev: (
Page 51 and 52: • BURSTALL Assume n, Ai,.. ., An,
Page 53 and 54: BURSTALL (iii) If E is 11E1 and D c
Page 55 and 56: BURSTALL j=CYCLICREVERSE(1) (*(/->n
Page 57 and 58: BURSTALL Our previous discussion de
Page 59 and 60: BURSTALL Taking the case where f2 c
Page 61 and 62: 13URSTALL In the case of cons and a
Page 63 and 64: 13URSTALL k=SUBST(i, a, j). Substit
Page 65 and 66: BURSTALL Eilenberg, S. & Wright, J.
Page 67 and 68: 3 Proving Compiler Correctness in a
Page 69 and 70: MILNER AND WEYHRAUCII and q, else r
Page 71 and 72: MILNER AND WEYHRAUCH We use `8e for
Page 73 and 74: I MILNER AND WEYHRAUCH ((JF&(count(
Page 75 and 76: MILNER AND WEYIIRAUCH (iii) For eac
Page 77 and 78: MILNER AND WEYHRAUCII We have abbre
Page 79 and 80: MILNER AND WEYHRAUCH give us a feel
Page 81 and 82: MILNER AND WEYIIRAUCII APPENDIX 1:
Page 83 and 84: .71 APPENDIX 3: proof of the McCart
Page 85 and 86: HDIIVIEHA3M CENIV 11UNIITAI I 1 1 1
Page 87: COMPUTATIONAL LOGIC
Page 90 and 91: COMPUTATIONAL LOGIC N((±)P(ti, t
Page 92 and 93: COMPUTATIONAL LOGIC (3) Find the di
Page 94 and 95: COMPUTATIONAL LOGIC are number term
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COMPUTATIONAL LOGIC A set of litera
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COMPUTATIONAL LOGIC Conditions 4 an
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COMPUTATIONAL LOGIC In our opinion,
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COMPUTATIONAL LOGIC Theorem 3. If S
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COMPUTATIONAL LOGIC and V. and furt
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COMPUTATIONAL LOGIC Kowalski, R.K.
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COMPUTATIONAL LOGIC another. It is
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COMPUTATIONAL LOGIC how the effect
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COMPUTATIONAL LOGIC The enlarged al
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COMPUTATIONAL LOGIC being within Pr
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6 The Sharing of Structure in Theor
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BOYER AND MOORE of a substitution S
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BoYER AND MOORE Otherwise TERM is n
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BOYER AND MOORE binding environment
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BOYER AND MOORE TERMB,INDEXB in the
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BOYER AND MOORE set INDEXB to INDEX
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H110011 CINV /13A0£1 21 .V, - cs'
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BOYER AND MOORE UNIFY can be made t
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7 Some Special Purpose Resolution S
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KUEHNER resolvent in D. Let C1 and
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KUEHNER obtained by deleting the gi
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KUEHNER D be any sPu-refutation of
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KUEHNER BI-DIRECTIONAL SPU/SNL RESO
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KUEHNER of finding a refutation of
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8 Deductive Plan Formation in Highe
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DARLINGTON and `c3' are set variabl
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DARLINGTON submitted to our theorem
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DARLINGTON Some further problems wh
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DARLINGTON Hewitt, C. (1971). Proce
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9 G-deduction D. Michie, R. Ross an
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MICIIIE, ROSS AND SHANNAN Search oc
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MICHIE, ROSS AND SHANNAN root node
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MICHIE, ROSS AND SHANNAN Positive c
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MICHIE, ROSS AND SHANNAN mere insta
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MICHIE, ROSS AND SHANNAN G-deduct i
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MICHIE, ROSS AND SHANNAN (4) additi
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MICHIE, ROSS AND SHANNAN (4) repres
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MICHIE, ROSS AND SHANNAN completene
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MICHIE, ROSS AND SHANNAN RESULTS Th
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MICHIE, ROSS AND SIIANNAN and, more
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• MICHIE, ROSS AND SHANNAN DM {{P
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S a Skolem constant T THERE Variabl
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INFERENTIAL AND HEURISTIC SEARCH se
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INFERENTIAL AND HEURISTIC SEARCH 0
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INFERENTIAL AND HEURISTIC SEARCH in
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INFERENTIAL AND HEURISTIC SEARCH no
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INFERENTIAL AND HEURISTIC SEARCH Re
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INFERENTIAL AND HEURISTIC SEARCH th
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INFERENTIAL AND HEURISTIC SEARCH be
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INFERENTIAL AND HEURISTIC SEARCH h
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INFERENTIAL AND HEURISTIC SEARCH so
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INFERENTIAL AND HEURISTIC SEARCH BI
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INFERENTIAL AND HEURISTIC SEARCH FI
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INFERENTIAL AND HEURISTIC SEARCH Em
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INFERENTIAL AND HEURISTIC SEARCH ob
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INFERENTIAL AND HEURISTIC SEARCH Co
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INFERENTIAL AND HEURISTIC SEARCH mo
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INFERENTIAL AND HEURISTIC SEARCH EP
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INFERENTIAL AND HEURISTIC SEARCH TH
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INFERENTIAL AND HEURISTIC SEARCH Sa
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INFERENTIAL AND HEURISTIC SEARCH no
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INFERENTIAL AND HEURISTIC SEARCH (a
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• • 0 • • • KO • •
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INFERENTIAL AND HEURISTIC SEARCH an
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• INFERENTIAL AND HEURISTIC SEARC
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INFERENTIAL AND HEURISTIC SEARCH (a
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• INFERENTIAL AND HEURISTIC SEARC
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INFERENTIAL AND HEURISTIC SEARCH °
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—AO INFERENTIAL AND HEURISTIC SEA
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• • • A • • 0 • • •
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INFERENTIAL AND HEURISTIC SEARCH pr
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• • • • • INFERENTIAL AND
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INFERENTIAL AND HEURISTIC SEARCH di
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,0* INFERENTIAL AND HEURISTIC SEARC
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INFERENTIAL AND HEURISTIC SEARCH cr
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INFERENTIAL AND HEURISTIC SEARCH se
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INFERENTIAL AND HEURISTIC SEARCH Tr
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INFERENTIAL AND HEURISTIC SEARCH ex
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INFERENTIAL AND HEURISTIC SEARCH 2.
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INFERENTIAL AND HEURISTIC SEARCH CO
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INrERENTIAL AND HEURISTIC SEARCH Ta
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• 0.00 1.00 2.00 3.00 4.00 Figure
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• to School 1 hool ,----- \ 4,% 3
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INFERENTIAL AND HEURISTIC SEARCH Ob
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INFERENTIAL AND HEURISTIC SEARCH Sp
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INFERENTIAL AND HEURISTIC SEARCH (i
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INFERENTIAL AND HEURISTIC SEARCH Ta
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INFERENTIAL AND HEURISTIC SEARCH Ta
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INFERENTIAL AND HEURISTIC SEARCH an
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INFERENTIAL AND IIEURISTIC SEARCH B
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INFERENTIAL AND HEURISTIC SEARCH Co
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INFERENTIAL AND HEURISTIC SEARCH of
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15 Mathematical and Computational M
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FRIEDMAN from base tree to surface
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FRIEDMAN Who did Jack find out that
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FRIEDMAN only. All computer runs we
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FRIEDMAN control program can be wri
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FRIEDMAN APPENDIX A "COMPUTER EXPER
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FRIEDMAN APPENDIX B "COMPUTER EXPER
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16 Web Automata and Web Grammars A.
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ROSENFELD AND MILGRAM (4) co' is ob
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ROSENFELD AND MILGRAM is applied, p
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ROSENFELD AND MILGRAM 7 I'S 0(Y, Y)
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ROSENFELD AND MILGRAM (5) If the ab
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ROSENFELD AND MILGRAM 3.4 Web gramm
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ROSENFELD AND MILGRAM where (11) ap
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ROSENFELD AND MILGRAM (d) Nog={ml,m
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ROSENFELD AND MILGRAM out that the
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17 Utterances as Programs D. J. M.
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DAVIES AND ISARD complex situation
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DAVIES AND ISARD and PLANNER (Hewit
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DAVIES AND ISARD which are consider
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DAVIES AND ISARD questions, and the
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DAVIES AND ISARD To help clarify ou
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DAVIES AND ISARD numbername(term(un
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DAVIES AND ISARD and a command, we
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PERCEPTUAL AND LINGUISTIC MODELS sl
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PERCEPTUAL AND LINGUISTIC MODELS 2.
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PERCEPTUAL AND LINGUISTIC MODELS an
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PERCEPTUAL AND LINGUISTIC MODELS 4.
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PERCEPTUAL AND LINGUISTIC MODELS (f
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PERCEPTUAL AND LINGUISTIC MODELS It
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PERCEPTUAL AND LINGUISTIC MODELS Le
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PERCEPTUAL AND LINGUISTIC MODELS He
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PERCEPTUAL AND LINGUISTIC MODELS ha
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PERCEPTUAL AND LINGUISTIC MODELS Th
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PERCEPTUAL AND LINGUISTIC MODELS wh
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PERCEPTUAL AND LINGUISTIC MODELS jo
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PERCEPTUAL AND LINGUISTIC MODELS Fi
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20 Approximate Error Bounds in Patt
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ITO (1) Proof of Pe ‹. Q„ We co
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ITO Q0=1-11 p(x)[p(ci I x)- p(c21x)
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ITO Thus we have proved eq. (49). U
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21 A Look at Biological and Machine
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GREGORY logical operations than are
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GREGORY no created contours, althou
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GREGORY black and the white illusor
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GREGORY appear trivial. There is no
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22 Some Effects in the Collective B
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VARSHAVSKY The set of automorphisms
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VARSHAVSKY that after each play of
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VARSHAVSKY do not use recessive str
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VARSHAVSKY M,\ M" .... - 397 Figure
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VARSHAVSKY Figure 2 I automata-- 1
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Forming the balance equation, we ha
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VARSHAYSKY This obviously suggests
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VARSHAVSKY This obviously suggests
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PROBLEM-SOLVING AUTOMATA be related
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, PROBLEM-SOLVING AUTOMATA either t
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PROBLEM-SOLVING AUTOMATA room; thus
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PROBLEM-SOLVING AUTOMATA Execution
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PROBLEM-SOLVING AUTOMATA as PLANNER
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PROBLEM-SOLVING AUTOMATA Table I. E
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PROBLEM-SOLVING AUTOMATA probably b
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PROBLEM-SOLVING AUTOMATA expanded w
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PROBLEM-SOLVING AUTOMATA extent tha
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PROBLEM-SOLVING AUTOMATA actions of
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PROBLEM-SOLVING AUTOMATA The algori
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PROBLEM-SOLVING AUTOMATA interest.
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PROBLEM-SOLVING AUTOMATA be that AI
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PROBLEM-SOLVING AUTOMATA Finally a
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PROBLEM-SOLVING AUTOMATA advantage.
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PROBLEM-SOLVING AUTOMATA Why should
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PROBLEM-SOLVING AUTOMATA A line in
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PROBLEM-SOLVING AUTOMATA places whe
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PROBLEM-SOLVING AUTOMATA scene. But
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PROBLEM-SOLVING AUTOMATA 4. The sys
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PROBLEM-SOLVING AUTOMATA Let me see
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PROBLEM-SOLVING AUTOMATA LEARNING T
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PROBLEM-SOLVING AUTOMATA pedestal n
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PROBLEM-SOLVING AUTOMATA relationsh
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PROBLEM-SOLVING AUTOMATA relations.
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PROBLEM-SOLVING AUTOMATA program bo
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PROBLEM-SOLVING AUTOMATA MOVE. To m
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PROBLEM-SOLVING AUTOMATA CHOOSE-TO-
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PROBLEM-SOLVING AUTOMATA Moving in
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25 The Mark 1.5 Edinburgh Robot Fac
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BARROW AND CRAWFORD or more element
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BARROW AND CRAWFORD reduce this to
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BARROW AND CRAWFORD SATELLITE COMPU
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BARROW AND CRAWFORD DATA READY ACCE
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BARROW AND CRAWFORD or contents alt
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movETo(x, y); BARROW AND CRAWFORD p
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BARROW AND CRAWFORD are performed b
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INDEX Abe 307, 323 ACE 3, 4, 6, 10,
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Jensen 78, 132 Johnson 245 Jordan 1
Page 503:
Steinberg 247 Stephenson 367 Strach
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