explicit control of reasoning mit document

8/13/2019 Explicit Control of Reasoning MIT Document

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MASSACHUSETTS INSTITUTE OF TECHNOLOGYARTIFICIAL INTELLIGENCE LABORATORY

Memo No. 4 2 7 June 1 9 7 7

EXPLICITCONTROLOF REASONING

by

Johan d e Kleer, Jon Doyle~,

Guy L . S tee le Jr.~,and Gerald Ja y Sussman

Abstract:

The construction of expert problem-solvings ys tem s requires the development oftechniques for using m odu lar representations of knowledge without encounter ingcombinatorial explosions in the solution effort. This report describes a n approach todealing with this problem based o n mak ing som e knowledge which is usua l ly implicitly part

of an expert problem solver explicit, thus al lowing thisknowledge about control to b emanipulated and reasoned about. Th e basic components of thisapproach involve usingexplicit representat ionsof th econtrol structureof the problem solver, and linking this andother knowledge manipulated by th eexpertby m ean s of explicitdata dependencies.

Fannie and John Hertz Found at ion Fellow

NSF Fel low

This research w a s conducted at th e Artificial Intelligence Laboratory of th e M assachusettsInstitute of Techno logy . Suppor t for the Laboratorys artificial intelligence research isprovided in part by th e Advanced Research Projects Agency of the Depar tment of Defenseunder Office of Naval Research contractnumber N 000 1 4 -75 -C -064 3 .


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de Kleer, Doyle, S tee le & Sussman 2 Explicit Control of R eason ing

Acknowledgements:

We thank Char les Rich, Marvin Minsky, Drew McDermott, Richard Sta l lman,Marilyn McLennan, Richard Brown, Peter Szolovits, and Gerald Roylance for suggestions,ideas and comments u s e d in this paper. Jon Doylei s supported by a Fannie and JohnHertz Foundation graduate fel low ship. Guy S tee le is supported by a National S cienceFoundation graduate fel lowship. This r e sea rch w as conducted at th e Artificial IntelligenceLaboratory of th e Mas sachusetts Institute of Technology. Suppor t for th e LaboratorysartificialIntel l igence research is provided in part by th e Advanced Research ProjectsAgency of th e Depar tmentof Defenseunder Office of Naval Research contract numberN00014-75-C-0643.

This paper will b e presented a t the ACM Conference on Artificial Intel

ligence and Programming Languages, Rochester, New York, August 1977.

C o n t e n t s :

The Problem 3

OurApproach 3Explicit Control Assertions 5Explicit Data Dependencies 7

The AMORD Language 8Primitives &Examples 9

The BLOCKS World 1 0Problem So lver Strategies 1 2Implementation of a R ef inem ent-P lanning Problem Solver 1 3Conclusions 1 7Notes 1 8Bibliography 22


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de Kleer, Doyle,S tee le & Sussman 3 Explicit Control ofR eason ing

TheProblem

A goal ofArtificial Intelligence is to construct a n advice taker,~~T a k a r aprogram which can b e told n ew knowledge an d advised about ho w that knowledge may b euseful. One approach toward achieving thisgoal h a s b e e n to u s e additive formalisms forthe represen tation of knowledge. Those formal ismsder ived from m athemat ical logic havebeen th e most popular. Unfortunately,the resulting sys tem s ar ecombinatorially explosive.Iti sdifficult to provide incremental guidance for problem solvers which u s e these additiveformalisms because of the unsolved question of how to describe knowledge abou t how toprofitably u s e other knowledge.Mdt~~~KflOW~adga

Substantial progress has b e en m a de in constructing expert problem solvers forlimited domains by abandoning th e goal of incremental addi t ion of knowledge. Experts

have usually been constructed a s procedures w hos e control structure embodies both th eknowledgeof th e p rob lem dom ain and how it is to b e u s e d . Th e proceduralembedd ing ofknowledge 0cSd U reS paradigm see m s naturalfor captur ing the knowledge of expertsbecauseof th e apparentcoherence w e observe in the behav ior of a human exper t who istrying to solve a p rob lem. Fo r e a c h specific problem h e see m s to b e following a definiteprocedure with discrete s t e p s an d conditionals. In fact, a n expertwill often report that h isbehavior is co ntrol led by a precom piled procedure. One difficulty with this theory is theflexibilityof th e expert s knowledge. If one poses a n ew problem, differing only slightlyfrom on e which we have previously observed a n expert s o l v e , he willexplain h is newsolution a s th e resul t of executing a procedure differing in detai l from th e previous one. Itreally see m s that th e procedure is created o n the flyfrom a moreflexible b a s e of

knowledge.

We bel ieve that th e procedural explanation i s an artifact of th e explanationgenerator rather than a clue to the structureof the problem solving mechanism. Theapparentlycoherentbehavior of th eproblem solver m ay b e a c o n s e q u e n c e of th e individualbehaviors of a s e t of relatively independent agents.C0he~~As a n example of coherentbehavior on th e part of a problem solver constructed from incoherent knowledge sources,we cite the ope ration of th e EL electronics circuit analysis program.Et EL is constructedfrom a s e t of Independent demons,e a c h implementing s om e facet of electrical laws appliedto particular device types. Th e nature of knowledge In the electrical domain is such thatthe analysis of a particular circuit is highly constrained, and s o th e traces of performanceand explanations produced by EL are coherent. L ike Simons ant,~~~An t EL d isplayscomplex and di rected beha v iors which a re largely determined by the nature of th e terrain,that is , th e circuit.

Our Approach

We here present a problem solving m ethodology by which th e individualbehaviors of a s e t of Independent rules are coord inated s o a s to exhibitcoherent behavior


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d e Kleer, D o y l e , S t e e l e & S u s s m a n 4 ExplIcit Control of Reasoning

Thismethodology establishes a se t of conventions for writing rules, and a se t of features

which th e rule Interpreter must supply to support t h e se conventions. Ou r rules operate on adata base of facts. Each fact is constructed with a justification which describes how thatfact was deduced from antecedent facts.

The key to obtaining c o h e r e n c e is explicitly representing so m e of the knowledgewhich Is usually Implicitin a n expert s ys tem :

Weexplicitly represent t hecontrol s ta te of the problem solver. Fo r example, each goalIs ass erted and justified in terms of other goals and facts. W e distinguish variouskinds of goalsfor ded uction an d action to which different subsets of rules apply.These explicitgoals and theirjustifications a re u s ed in reasoningabou t th e problem

solver s actions and its reasons for d e c i s i o n s . hcit C o n t r o

Weexplicitly represent a s facts knowledge about ho w other facts ar e to b e used. Intraditional methods of representingknowledge the w a y a piece of knowledge is used isimplicit rather than something that c an b e r e a so ned about. In PLANNER, forexam ple, the u s e of a piece of knowledge is fixed at th e t ime that the knowledge isbuilt into th e problem solver, an d it is no t possible to later qualify th e u s e ofthisknowledge. One can specify a rule to b e u s ed a s either a consequent or antecedenttheorem, buto ne can no t laters a y But dont do that if ... is true.To allow th eexpression ofsuch statements so m e facts must b e assertions abou t other facts.

We explicitly represent t he r e a so n s for belief in facts. Each fact h a s associated

justif ications which describe reasons for believing that fact and ho w they depend onbeliefs in other facts and rules. A fact is believed ifi t h a s wel l - founded support interms of other facts an d ru les .W -Founded S u p p o r t The current ly active data b a s e contextis defined by th e s e t of primitive premises and assumptions in force.

The justifications can b e u s ed by both the usera nd the problem solver to gaininsight into th e operation of th es e t of r u le s o n a particular problem. Oneca n perturb thepremises and examine th e changed beliefs that result. This is precisely wh a t is needed forreasoning about hypothetical situations. Onec an extract information Tram th ejustification s in th e analysis of error conditions resulting from incorrect assumptions. Thisinformation can b e u s e d in dependency-directed b a c ktrack ing~ktr8~~to pinpoint th e

faulty assumpt ions and to limit future s e a r c h .

Theexplicit data dependencies allow u s to control the connection between controldecisions and th e knowledge they are b a se d

0~~SeParotIonW e ca n separate th e reasons for

belief in derived facts from the control decisions affecting their derivation when the factsare independent of th e control decisions. Anomalous dependencies a re produced when thisseparation Is not mad e. I n chronological backtrackingU1~0 A N N E R control decisions areconfused with th e logical grounds for belief in facts. Thisresults in ~heloss ofuseful


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d e K l e e r , D o y l e , S t e e l e & S u s s m a n 5 Explicit Control of R eason ing

Information when contro l decisions ar e changed.

Thistechnique of using explicit control knowledge to guide a problem solver doesn o t r e s o l v e a l l difficulties, since it is often unclear a s to wh a t knowledge is usefully madeexplicit. In th e following we present examples o f th e u s e of explicitcontrol knowledge inconstructingcoherentbehaviors from incoherent knowledge sources.~~0ntr0IVocobulary

Explicit C o nt r o l Assertions

S u p p o s e w e k n o w a f e w s i m p l e f a c t s , which w e ca n express in a bastard form ofp r e d i c at e c a l c u l u s :

(> (human :x) (fallible :x)) Everyhumanisfallible!

(hunan Tur Ing) Poor Turing.

Ifprovided with a simple syntactic s y s t em with tw o d er ivation rules (which wemay I n t e r p r e t t o b e t h e conjunction introduction and modus ponens rules of logic),

A ( . . . > A B )

B A

(ANOAB) B

then by application of t h e se rules to th e given facts w e m ay der ive theconclusion

(A N D (faHible Turing) (human Turing)).

Since th e rules are sound, we may bel ieve thisconclusion.

Severa l m ethods can b e u s ed to mechanically der ive thisconclusion. One scheme(the British Museum Algorithm)I s to make a ll possible derivations from th e given factswith th e given rules of inference. These c an b e enumerated breadth-first. If th e desiredconclusion Is der ivable, Itwilleventually appear an d w e can turn offo ur machine.

The difficulty with this approach is t h e l a r g e n u m b e r of deductions made whichare either irrelevant to th e desired conclusion (they d o notappear in its derivation) or

u se l e s s , producing an incoherent performance. For instance, in addition to th e a b o v e ,conjunction introduction will produce s u c h wonders~

( AN D ( h u m an T u r in g ) ( hu m an T u r i n g ) )

(AND (> ( h u m a n : y ) (f a l l i b l e :y ) ) ( hu m a n T u r i n g ) )

The literature of mechanical theorem-proving ha s concentrated o n sophist icated


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d e K l e e r , D o y l e , S t e e l e & S u s s m a n 6 E x p l i c i t C on tr ol o f R e a s o n i n g

d e d u c t i v e a l g o r i t h m s a n d p o w e r f u l b u t g e n e r a l i n f e r e n c e r u l e s w h i c h l i m i t t h e

combinatorial explosion. These combinator ial strategies a re not sufficient to limittheprocess e n o u g h t o p r e v e n t c om p ut at i on al catastrophe. Verily, a s much knowledge is neededt o e f f e c t i v e l y u s e a f a c t a s there is in the fact.

Consider the problem of controlling wh a td eductions to make in th e previousexample s o that only relevant conjuncts a re der ived. The d er ivation rules can b e modifiedt o i n c l u d e i n t h e a n t e c e d e n t a s t a t e m e n t t h a t t h e c o n s e q u e n t i s n e e d e d :

( S H O W ( A N D A B ) ) ( S H O W B )

A (->AB)

B A

(ANOAB) B

G i v e n t h e s e r u l e s , o n l y relevant conclusions a re generated. Th e assertion (S H O W X) s a y snothing about th e truth or falsity of X, but rather Indicates that X is a fact which should

be derived If possible. Since th e S H O W r u le s only deduce n e w facts when interest in themhas been asserted,explicit d er ivation r u le s are n e eded to ensure that ifinterest in some factis asserted, interest is a l s o a s se r t e d in appropr iate a n t e ce den t s of it. This is how subgoalsare generated.tm~tb0~

(S H O W ( A N D A B ) ) ( S H O W ( A N D A B ) )

A

(S H O W A )

(S H O W B )

(S H O W B )(-> A B )

(S H O W A )

With these rules the d er ivation p r o ce s s is constrained. To derive

(AND (fallible Turing) (human Turing)),

interest must be firstasserted:

(S H O W (AND ( f a l l i b l e Tu r in g ) ( hu m an T u r i n g ) ) ) .

A p p l i c a t i o n o f t h e d e r i v a t i o n r u l e s n o w r e s u l t s i n t h e f o l l o w i n g s e q u e n c e o f f a c t s :


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de Kl e e r , D o y l e , S t e e l e & S u s s m a n 7 Explicit Control of R eason ing

( S H O W (fallible Turing))( S H O W ( h u m a n T u r i n g ) )

( f a l l i b l e Turing)

(A N D (fallible Turing) (human Turing))

These a r e a b s o l u t e l y a l l t h e f a c t s t h a t ca n b e d e r i v e d , a n d n o facts were derived which weren o t r e l e v a n t t o t h e g o a l .

Explicit Data Dependencies

Thisapparent coherence h a s b e e n achieved by th emanipulation ofexplicitcontrol assertions. Th e u s e of explicitcontrol n e ce s s i t a te st he u s e of explicitdependencies.I f t h e c o n c l u s i o n s o f a r u l e o f i n f e r e n c e u n i fo r m ly d e p e n d e d o n t h e a n t e c e d e n t s o f t h e r u l e

t h e n S H O U r u l e s w o u l d c a u s e b e l i e f i n t h e i r c o n s e q u e n t s t o d e p e n d o n t h e s t a t e m e n t o finterest i n t h e m . That i s wr on g . I f t h e t r u t h o f a s t a t e m e n t d e p e n d s o n t h e t r u t h o f t h eneed f o r i t , t h e s t a t e m e n t l o s e s s u p p o r t i f i n t e r e s t i n i t i s wi th d r aw n. Ev e n w o r s e , i f aderived conclus ion is Inconsistent, one might accidently blame th e deducer forh is curiosityi n s t e a d o f t h e f a u l t y a n t e c e d e n t o f t h e c o n t r a d i c t i o n ! The d e p e n d e n c e o f e a c h n e w

c on c lus i on o n o t h e r b e l i e f s m u s t b e m a d e e x p l i c i t s o t h a t t h e d ep en d en c i es o f c o n t r o l

a s s e r t i o n s ca n be s e p a r a t e d from t h e r e a s o n s for derived results. I n t h e c on j un c ti onIntroduction r u l e , t h e t r u t h o f t h e c o n j u n c t i o n d e p e n d s o n l y o n t h e t r u t h o f t h e c on j un c tsbut interest in th e truth of th e conju ncts propagates from interest in th e truth of th econjunction.

We c a n d e p i c t t h e r u l e s o f inferencefor truth an d control with th e correctdependency i n f o r m a t i o n a s f o l l o w s :

(AND A B))

B )

(-> A B ) ( S H O W B )

(S H O W A )

In this diagram, th e targetstatem ent is derived if the s o u r ce statements ar e known . Onlyt h e s o l i d a r r o w s r e p r e s e n t d e p e n d e n c y l i n k s .


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de Kleer, Doyle, S tee le & Sussman 9 ExplicitControl of Reasoning

fact. If th e assumed fact is contradicted and removed by backtracking,t he negation of theassumed fact is asserted an d supported by the r e a so n s under ly ing th econtrad ic tion.~~~05 00d

E x a m p l e s

The forward version of conjunction introdu ction is implemented in AMORD a sthe following rule:

(Rule (:f :a)(Rule (:g :b)

(Assert ( A N D : a : b ) ( & + : f : g ) ) ) )

To paraphrase this rule, the addition of a fact f with pattern a intoth edata-base results in

the addition of a rule which checks every fact g in t he data-base and asserts thec o n j un c t i o n o f a an d t h e pattern b of g. Thus if A Is asserted, so will be (A N D A A), (ANOA ( A N O A A)), ( AN D (A N D A A ) A ), e tc . Note that th e atom A N D is no t a distinguishedsymbo l .

Tocontrol theseded uct ions, the above rule c an b e replaced by th e following rulewhich effects consequent reasoning about conjunctive g o a l s .

( Ru l e (: g (S H O W ( A N D : p : q ) ) )

( R u l e ( : c ] . :p)

( R u l e ( : c 2 : q )

( A s s e r t ( A N O : p : q ) ( & + : c 1 . : c 2 ) ) )

( As s e r t ( S HO W : q ) ( ( B C & + ) : g : c l ) ) )

( A s s e r t (SHOW : p ) ( ( B C & + ) : g ) ) )

I n t h i s r ul e t h e c o n t r o l s ta tements (S H O W s) d e p e n d on belief inthe relevant controlled facts

so that the existence of a subgoal forth e second conjunctof a conjunctive goaldepends ont h e s o l u t i o n for th e firstconjunct. At th es am e t ime, n o controlled facts depend o n controlf a c t s , s i n c e t h e justification for a con junction is entirely in terms of the conjuncts, and noto n t h e need f o r d e r i v i n g t h e c o n j u n c t i o n . Thismeans that the control over the derivation

o f f a c t s cannotaffect th etruth of th e derived facts. Moreover, the hierarchy of nested,lexically scoped rules allows th e s pecification of sequencing and restr iction Information. F o ri n s t a n c e , t h e above r u l e c o u l d have been written a s

( Ru l e ( : g ( S H O W ( A N D : p : q ) ) )

( Ru l e (: c l : p )

(Rule (:c2 :q)(Assert ( A N D : p : q ) ( & + : c ] . :c2))))

(As s e r t (SHOW : p ) ( ( B C & + ) : g ) )

( A s s e r t (SHOW : q ) ( ( B C 6 + ) i g ) ) )


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de Kleer, Doyle, S tee le & S u s s m a n 1 0 E x p l i c i t Controlo f Reason ing

T h i s f o r m of th e rule would a l s o only der ive corrects ta tem en t s , but would no t b e as tightlycontrolled a s th e previous rule. In thisc a s e , both subgoals are asserted immediately,although there isn o reason to work on th e second conjunctunless the firstconjunct hasbeen solved. Thisform of the rule allows mo re work to be done in that th e possib le mutualconstraintsof th e conju ncts o n e a ch other due to shared variables is not accounted for.That Is , in th e first form of the rule, solutions to th efirst conjunctw e r e u se d to special izeth e subgoals for th e second conjunct, s o that th e constraints of th e solutions to the first areaccounted for in th e s e c o n d subgoal. In the s e c o n d form of th e rule much work mightb edone on solving e a c h subgoal independent ly, with the d er ivation of th e conjunctionperformed by an explicit m atch ing of t h e se derived r e su l t s . This allows solut ions to th esecond subgoal to b e der ived which cannot match an y solution to th e first subgoal.

Other consequent rules for Modus P o n e n s , Negated Conjunction Introduction,and Double Negation Introduction ar es imi lar in spirit to th e rule forC onjunctionIntroduction:

(Rule (:g ( S H O W :q))( R u l e (:i (> :p :q ) )

( R u l e ( : f : p )

( A s s e r t : q ( l I P : 1 : f ) ) )

( A s s e r t ( S H O W : p ) ( ( B C l I P ) : g : 1 ) ) ) )

(R u l e ( :g ( SH OW ( N O T ( A N D : p : q ) ) ) )( R u l e ( : t ( N O T : p ) )

( A s s e r t ( N O T ( A N O : p : q) ) ( 6 + : t ) ) )

( R u l e ( : t ( N O T :q ) )

( A s 8 e r t ( N O T ( A N D i p :q ) ) ( 6 + : t ) ) )

( A s s e r t (SHOW ( N O T : p ) ) ( ( B C 6 +) :g ))

( A s s e r t (SHOW ( N O T : q ) ) ( ( B C 6 + ) : g ) ) )

(R u l e (: g (S H O W ( N O T ( N O T : p ) ) ) )

(Rule (: f :p)(Assert ( N O T ( N O T : p ) ) (+ :f)))

(Assert (S H O W :p) ((BC -+) : g ) ) )

The BLOCKS World

Wewill d iscuss problem solving in t h e bl oc k s w o r l d a s an example of ourm ethodo logy . F ir s t, we formalize th e domain with a se t of logical axioms which express aMcCarthy-Hayessituational ca lcu lus .Shb0~ t I 0 f l 9 W e us ethe syntax (TRUE < s i t u a t i o n > ) t o s t a t e th at t h e i n d i c a t e d s t a t e m e n t h ol d s i n t h e indicated situation. TRU E is


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de K l e e r , D o y l e , S t e e l e & Sussman Ii Explicit Control ofR eason ing

a sy ntactic convenience. We could justa s wel l add a n extra argument to e a c h of th epredicates of the dom a in . Fo r example, t h e f o l l o w i n g a x i o m e xp r e s se s th e fact that in t h e

situation arrived at after a P U T O N operation t h e b l o c k w h i c h m o v e d i s o n t h e b lock It wa sp u t o n .

( A e s a r t (> ( A N D (TRUE ( C L E A R T O P ix) is)

(TRUE (S P AC E - F O R i x : y ) i s ) )

(TRUE ( ON : x : y ) ((PUTON : x : y ) . : s) ) )

(Premise))

More a x i o m s a r e needed for th eblocks wor ld . B locks no t moved by aP UT O Nr e m a i n on t h e i r f o r m e r s u p p o r t :

(Assert (>

( A N D (TRUE ( ON : a : b ) : s ) ( N O T (= : a :x)))(TRUE ( ON : a : b ) ((PUTON : x : y ) . : s ) ) )

( P r e m i s e ) ) .

A b l o c k i s said to b e C LEA RTO P if n o o t h e r block is O N it. We ass um e for simplicity thato n l y o n e b l o c k can b e ON a n o t h e r , a n d introduce statements of C LEA RTO P forblocks madeclear by PU TO N:

( A s s e r t (> ( A N D (TRUE ( ON : x :b) :s)( A N O ( N O T (. : b Table)) ( N O T ( : y s b ) ) ) )

(TRUE (C L E AR T O P : b ) ((PUTON : x : y ) . :8)))

(Premise)).

Ifa block is C LE A RTO P, it remains s o after a n yaction which d oe s not place anotherb lock O Nit.

(Assert (> ( A N D (TRUE ( C L E A R T O P :b) : s ) ( N O T ( : y :b)))

(TRUE (C L E AR T O P :b) ((PUTON : x : y ) . :s)))(Premise))

A b l o c k c a n b e ON o n l y on e other block.

(Assert (> (AND (TRUE ( ON : x : z ) : s ) ( N O T (ai : z : y ) ) )

( N O T (TRUE ( ON : x : y ) : s ) ) )(Premise))

Th e d e f i n i t i o n o f CL E ARTO P i s :


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de Kleer, Doyle,S tee le & Sussman 1 2 Explicit Control of R eason ing

(Assert (> (TRUE ( ON : x : y ) : s )(NO T ( TRU E (CLEA RTO P :y) is)))

( P r e m i s a ) ) .

If a block is CL EA RTO P, it ha s SPA CE-F O R an y other block.

(Assert (> (TRUE (C L E AR T O P : x ) : s )

(TRUE (S P AC E - F O R : y : x ) : s ) )

(P r e m i s e ) )

Ifa block I s n o t C L E A R TO P , i t d o e s n o t h a v e S P A C E -F O R a n yth i ng m o r e . This a s s u m e s o n l yo n e b l o c k c a n b e ON a n o t h e r .

(Assert (> ( A N D ( N O T (TRUE ( C L E A R T O P : x ) :s )) ( N O T ( :x Table)))( N O T (TRUE (S P AC E F O R : y :x) :s)))

(P r e m i s e ) )

The t a b l e always has S P A C E - F O R ev er yth i ng .

( A s s e r t ( T R UE ( S P A C E F OR : x Table) : s ) ( P r e m i s e ) )

We s e t u p an i n i t i a l s ta te of th e s y s t em by add ing situation-specif ic axiom s.

( A s s e r t (TRUE ( ON C A ) I N I T ) (Premise))( A s s e r t ( T RU E ( ON A Table) 1N I T) ( P r e m i s e ) )

( A s s e r t ( T RU E ( ON B T a bl e ) I N I T ) ( P r e m i s e ) )

( A s s e r t (TRUE (C L E AR T O P C ) I N I T ) ( P r e m i s e ) )

( A s s e r t ( T R UE ( C L E A R T OP B ) I N I T ) ( P r e m i s e ) )

Problem S o l v e r S t r a t e g i e s

There a r e a n u m b e r o f s t r a t e g i e s f o r u s i n g t h i s description of this blocks worldf o r problem solving. Consider the problem of finding a s e q uen ce of actions (PU TO Ns )which transformsth e initial situation into a situation in which b lock A is O N b lock B . Sucha sequence m ay b e derived from a constructive proof of the statement (EXISTS (S ) (TR U E(O N A B) 5)) from th e initial situation.~fl9t~~~ctI0fl

One s t r a t e g y i s to derivea ll possible c on sequences of th e axioms using the logicalrules of inference without S H O W restrictions. If thegoal s ta te is a p o s s i b l e f u t u r e o f t h eInitial state, then a solutIon s e q uen ce willeventually b e generated. Thisforward chainingstrategy generates piles of irrelevant s ta tes w h i c h , a l t h o u g h a c c e s s i b l e f r o m t h e initial state,a r e n o t o n a n y s o l u t i o n p a t h t o th egoal s ta te .


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A dualstrategy is backward chaining. This ca n b e accomplished using t h e S H O Wrules descrIbed previously to generate a ll p o s s i b l e p a s t s of t h e g o a l s t a t e . A l t h o u g h a l l t h es t a t e s s o g e n e r a t e d a r e r e l e v a n t t o t h e g o a l , m o s t o f t h e s e a r e I n a c c e s s i b l e from th e initialsItuation.~~~Fift.,,

R ef i n e m e n t p l an ni ng i s t h e s t r a t e g y o f d e c o m p o s i n g t h e p r o b l e m i n t o t h e

sequent ia l attainment of intermediate Islands o r s u b p r o b l e m s . ~ ~ 1 ~Both f o r w a r d an dbackwardchaining ar e special cases of thisstrategy, i n which the is lands proposed a rederived by finding s ta te s separated from the initialor goal s ta tes by th e application of asingle operator. Th e more general u s e is to propose subproblems which ar e not necessarilyi m m e d i a t e l y a c c e s s i b l e from t h e I n i t i a l o r g o a l s t a t e s , b u t w h i c h , i f s o l v e d , e n o r m o u s l y

restrict the size of the remaining subproblems. These intermediate subgoals ar e produceda t t h e r i s k of being either irrelevant to t h e g o a l o r i m p o s s i b l e t o achieve from th e initial

state, and s o must b e suggested by methods which know reasonable decomposit ions of adomain-specific nature.~SP~1BC

Severa l additional cons traints influence the se le c t i on of problem solver strategies.Many operator s e q u e n c e s haven o ne t effect (they a re composite no-ops). A problemsolver which fails to recognize that t h e se sequences produce n o change of s t a t e will loopunless Its search I s g lobal ly breadth-f i rst. In addit ion, it w i l l w a s t e e f f o r t deriving solutionsto problems isomorphic to o ne s it h a s already s o l v e d . To solve this p rob lem, i t i s i m p o r t a n tto represent th e propert ieso f situations in s u c h a way t h a t t w o s i t u a t i o n s w h i c h a r eidentical with respect to some p ur p o s e c a n b e recognized a s such.

I mplementation o f a R e f i n e m e n t -P l a n n i n g P r o b l e m S o l v e r

The principal difficultyo f so lv ing problems in wor lds which can have arbitrarilymany s t a t e s i s that any simple deduction mechanism willexplore a ll of them. Our problems o l v e r l i m i t s t h e p o t e n t i a l c o m b i n a t o r i a l e x p l o s i o n b y h a v i n g d o m a i n s p e c i f i c r u l e s which

control the introduction of n e w s t a t es . The problem solver a l s o contains rules which ared o m a i n i n d e p e n d e n t , o f w h i c h M o d u s P o n e n s a n d C o n j un c t i o n I n t r o d u c t i o n a r e e xa m p l e s .

These S H O W r u l e s w i l l o n l y b e I n v o k e d f o r q u e s t i o n s w h i c h concern a n existing s ta te . Theya r e n o t a l l o w e d t o g e n e r a t e n ew or hypothetical s ta tes .

Th e s t a t e m e n t ( G OAL < c o n d i t i o n > < s i t u a t i o n > ) i s a s s e r t e d w h e n w e w ant

to b e achieved in so m e s ituation which is a successo r of . Thefollowing rule is t r iggered by thisassertion an d controls the solution p r o ce s s . When t h egoal is satisfied this rule willassert (SATISFIED (G O A L < s i t u a t i o n > )) where is th ename of the situation w h e r e

no w holds. Th e subrule firstc h e c k s whether the goal is al ready true. Itasserts (TR U E ? < e l tuatI o n > ) ( a s k i n g t h e q u e s t i o n , I s t r u e o rfa lse In ?) and s e ts u p t w o r u l e s w h i c h w a i t f o r t h e a n s w e r . A c o n v e n t i o n o fou r rules Is thata n answer I s guaranteed. Processing the goal will continue when th e


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a n s w e r ( Y E S or N O ) is asserted. Ifthecondition i s n o t t r u e I n t h e c u r r e n t s i t u a t i o n , p l a n n i n gproceeds by as sert ing (A C H IE V E < s i t u a t i o n > < g o a l > ) , w h e r e i sthe fact name of th e goal. Th e A CH IEVE factstr igger th erelevant m ethods forach ievemento f t h e goal c o n d i t i o n . These m e t h o d s m a y i n t r o d u c e n ew s i t u a t i o n s an d p e r f o r m a c t i o n s .

I f a m e t h o d t h i n k s t h a t i t h a s s u c c e e d e d i n p r o d u c i n g a s u c c e s s o r s t a t e o f t h e g i v e n

situation inwhich th e goal condition is true It a s s e r t s ( A CH I EVED? < n e w situation>), where < n e w s i t u a t i o n > i s th es ituation in wh ich is thought to besatisfied. Th e g o a l rulethen checks thissuggestion with TRU E? and makes th e SAT 1SF!E Oa s s e r t i o n i f s u c c e s s f u l . I f t h e m e t h o d i s in error , the bug manifestat ion is noted in a B U Ga s s e r t i o n . T h i s i s m a r k e d a s a c o n t r a d i c t i o n a n d c a u s e s b a c k t r a c k i n g . A m o r e soph ist icatedproblem solver would at this point entera debugging strategy. The justification of th ec o n t r a d i c t i o n can b e t r a c e d . T h i s I n f o r m a t i o n i s h e l p f u l in d iagnosing th e fault andc o n s t r u c t i n g a p a t c h t o t h e d o m a i n s p e c i f i c m e t h o d s .

( Ru l e ( : g ( G O A L : c : a ) )

(Assert ( T R U E ? : c : s ) ( G o a l t r u e ? :g))( R u l e ( : q ( T R U E ? : c i s ) )

( Ru l e ( : t ( Y E S : q ) )( A s s e r t ( S A TI SF I E D ( G OAL : c : s ) : s )

(G o a l i m m e d s a t i s f i e d : g : t ) ) )

(Rule (:t (N O :q))(Assert (A C H IE V E :c : s : g ) ( G o a l u n s a t i s f i e d : g : t ) )

(Rule (:w (A CH IEVED ? :g :sl))(Assert (TRU E? :c :sl) (Did it succe ed? :g :t :w))(Rule (:q2 (TRU E? :c :sl))

(Rule (:f (Y ES :q2))(Assert (SATISFIED (G O A L :c :e) :sl)

( W i n : g : f ) ) )

(Rule (if ( N O : q2 ) )(Assert (B U G :g :w :f)

( C o n t r a d i c t i o n : w : f ) ) ) ) ) ) ) )

To c h e c k w h e t h e r a s t a t e m e n t i s t r u e i n a s i t u a t i o n t h e SHOW mechanism is used.

Theass ert ion of (G O A L ) r e q ue s t s to b e true ins o m e s u c c e s s o r s t a t e o f < s i t u a t i o n > . The s t a t e m e n t < c o n d i t i o n > m u s t b e r e l a t i v e t o asituational variable because it is checked in tw o (po tentially) different situations in th e G O A Lrule above. In order to testwhether this statementi s true or false this variable must b ebound to th e particular situation being considered. Th econdition of a G O A L asser t ion mustbe of the form (L ),( 1 . abbreviates L A M B D A ) where Is a predicate form wIth a n o p e n situational var iable . Theunification of th e trIggerpattern of TRU E? with the assertion ( TRU E? ) ha s th eeffect of binding the particular situation beingcons idered with th e situational var iable u s ed in . By lambda-


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abstracting th e goal condi t ion, w e eliminate th e explicit m ention o f a n y p a r t i c u l a r . s i tu at i oni n t h e g o a l d e s c r i p t i o n . E q u i v a l e n t g o a l s a r e v a r i a n t s , a n d s o w i l l b e i d e n t i f i e d b y t h e

AMORD ~ G o a ls

( Ru l e (: g (TRUE? ( L : s : p ) : s ) )

( R u l e ( : f : p )

(Assert ( Y E S : g ) (Return : g : f ) ) )

( R u l e ( : f ( N O T : p ) )

(Assert ( N O : g ) ( R e t u r n : g : f ) ) )

( A s s e r t (SHOW : p ) ( T r y p o s i t i v e : g ) )

( A s s e r t ( SHO W (N OT : p ) ) (T r y n e g a t i v e i g ) ) )

I f t h e g o a l i s a c o n j u n c t i o n o f c o n d i t i o n s , t h e f o l l o w i n g r u l e i s t r i g g e r e d . Some

conjunctive g oa l s can b e a c h i e v e d b y a c h i e v i n g e a c h c o n j u n c t s e p a r a t e l y . T h i s i s c a l l e d aL I N E A R P L A N . S o m e t i m e s t h e c o n j u n c t s c a n b e a c h i e v e d i n o n e o r d e r bu t n o t i n t h e o t h e r

order.~80A c o n j u n c t i v e g o a l c a n n o t a l w a y s b e d e c o m p o s e d i n t h i s wa y . ~ 0 m 0 b 0 ~ ~ *I n t h e c a s e

o f s u c h a n o n - l i n e a r p r o b l e m , o u r r u l e f a i l s .

( R u l e ( : f ( A C H I E V E ( L : s ( A N D : c l :c 2) ) : s l : p u r p o s e ) )

( As s u m e ( LI N EA R P L AN : f ) ( F i r s t - o r d e r : f ) )

( Ru l e ( : p ( L I N E A R - P L A N : f ) )

( A s s u m e ( S T A T E D O R D E R : p ) (C o n j u n c t - o r d e r : p ) )

( R u l e ( : o ( S T A T E D - O R D E R : p ) )

(Assert ( O R D E R E D - P L A N : s : c l :c2 : s l : p u r p o s e ) (Try :o)))

( R u l e ( : o ( N O T (S T AT E D O R DE R : p ) ) )

(Assert ( O R D E R E D P L A N : s :c 2 : c l : s l : p u r p o s e ) ( T r y : o ) ) ) )

( Ru l e ( : p ( N O T ( L I N E A R - P L A N : f ) ) )

This problem solver h a s n o clever ideas about thiscase .

( A s s e r t (FAIL : p ) (C o n t r a d i c t i o n : p ) ) ) )

Th e n e x t r u l e r e f i n e s a c o n j u n c t i v e g o a l a s a n o r d e r e d l i n e a r p l a n . I t p r o d u c e s

t h e s u b g o a l of f i n d i n g a n i s l a n d i n which t h e f i r s t c o n j u n c t i s t r u e . I f t h e f i r s t s u b g o a l

c a n b e s a t i s f i e d , I t t h e n e s t a b l i s h e s t h e s u b g o a l o f s a t i s f y i n g t h e s ec on d c o n j u n c t i n a

successor ofthis is land. If th e s e c o n d subgoal ca n be sa tisfied the resulting s ta te isproposed a s a so lution to th e conjunctive g o a l . The goal rule which tr iggered this m ethodi s r e s u m e d b y t h e s t a t e m e n t ( AC H I EV E D? < p u rp o s e > ) which t e s t s

( u s i n g T R U E ? ) t h e o r i g i n a l g o a l c o n d i t i o n i n < n e w - s i t u a t i o n > . I f t h i s method i s w r o n g .t h e G O A L r u l e w i l l f a i l .


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( R u l e (if ( A C H I E V E ( L : s ( T R U E (CLEARTOP : y ) :8)) : s l : p u r p o s e ) )(Rule (:o (TRU E ( O N :x : y ) : s i ) )

(Assert (AC H I E VE ( L : u ( N O T ( T R U E ( ON : x : y ) : u ) ) ) :s l : p u r p o s e )

( I l a k e C L E A R TO P : f : o ) ) ) )

Th e m e t h o d s i n t r o d u c e s o m e i n c o m p l e t e n e s s t h a t wa s n o t p r es ent i n t h e o r i g i n a l

a x i o m s . I n r e t u r n t h e p r o b l e m s o l v e r a l w a y s h a l t s b y r un ni ng o u t o f f u r t h e r r u l e s t o r u n .

The m a i n r e a s o n t h e s p e c i f i c m e t h o d s c o u l d b e u s e d s u c c e s s f u l l y i s t h a t t h e d e d u c t i o n s a r e

e x p l i c i t l y c o n t r o l l e d b y c o n t r o l a s s e r t i o n s ( G O A L , A C HI EVE , A C HI EV ED ?, T R U E ? ) .

Conclusions

Many kinds of com binator ia lexplosions ca n b e avo ided by a problem so lver thatthinks about wh a t it is trying to do. In orderto b e able to meditate on it s goals, act ions andreasons for belief, t h e se must b e explicitlyrepresented in a form manipulable by th edeductive process. In fact,this internal control domain is a problem domain formalizedusing assert ions and rules just likea n externaldom ain. How can we u s e assertions aboutcontrol states to effectivelycontrol the d educt ive p r ocess?

The key to this problem is a s e t of conventions by which th eexplicit controlassert ions are u s e d to restr ict th e application of sound but otherwise explosive rules. Theseconventionsare supported by a vocabulary of control c o n ce p t s and a se t of systemic

features. Theapplicability of a rule c an b e restricted by em bedding it in a rule having apattern which matches a control assertion a s a n entrance condition. Th e rule languageal lows the var iables bound by m atch ing thecontrol assertions to further restr ict th ee m be d d e d rule. But we w ant the conclusions of sound r u le s to depend only o n their correctantecedents and not o n th e control assertions u s ed to restrict their derivation. This isnecessary to enable fruitfuldeliberations aboutthe r e a so n s for belief in a n assertion. Thesystem must provide means for describing the r e a so n s for belief in a n assertion and meansfor referringto an object of belief.

Somet imes it is n e ce s sa r y to make assumptions --to a c c e p t beliefs that m ay laterbe discovered false. Conclusions of r u le s which operate with incomplete know ledge must

depend upon th e control assum ptions m ade . Accurate dependencies al low preciseassignment o f respon sibi li ty for incorrect beliefs. This i s n e ce s sa r y for efficient search andperturbation analysis.


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Notes

A d v i c e Tak er

The t e r m A d v i c e T a k e r o r i g i n a t e s w i t h McCarthy [ 1 9 6 8 ) .

A d d i t i v e K n o w l e d g e

I s it p o s s i b l e t o havea n a d d i t i v e s y s t e m i n w h i c h k n o w l e d g e a b o u t o t h e r

knowledge can b e expressed? Sometimes advice m a y b e negative. For example, th e processof sorting a l ist m ay b e defined a s findinga permutation of the l ist which is ordered. Anobvious procedure derived from thisdefinition is that o f e n u m e r a t i n g t h e p e r m u t a t i o n s o ft h e l i s t a n d t e s t i n g e a c h f o r o r d e r . I f b e t t e r m e t h o d s b e c o m e k n o w n , w e w i l l want t o g i v e

t h e a d v i c e t h a t t h i s method s t i n k s . How c a n t h i s b e a n a d d i t i v e p i e c e o f k n o w l e d g e ?Perhaps a w ay to make such knowledge additive is to formal ize the state of mind of th eproblem solver , and le t such advice changei ts s ta te of m ind .

ProceduresThe Procedural Embedding of Knowledge Is the phi losophy popularized by

Winograd [ 1 9 7 2 ) and Hewitt [ 1 9 7 2 , 1 9 7 5 ) that knowledge c an b e m os t profitably represented

a s computer p rograms.

CoherenceIn Human Problem Solving[Newel l and Simon 1 9 7 2 ), the apparently coherent

behavior of human subjects is a l s o explained in te rm s of a se t of relatively independentagents (formalized a s productions). Minsky [1 9 7 7 ) proposes a structure for human behaviorin terms of a society of agents.

ELEL is a se t of rules for electrical circuit analysis wh ich embodies the method of

propagation of constraints. {Sus sm an an d Stal lman 1 9 7 5 )EL is implemented in A R S .[Stailman and Sussman 1 9 7 6 )

S i m o n s An t

S i m o n [ 1 9 6 9 ] p oi nt s o u t t h a t a p p a r e n t l y c o m p l e x b e h a v i o r can r e s u l t f r o m s i m p l e

p r o c e d u r e s op er at i ng i n a c o m p l e x b u t c o n s t r a i n i n g domain.

Explicit ControlP r o d u c t i o n System d e v o t e e s h a v e t e n d e d t o approach t h e p r o b l e m o f c on tr ol

t h r o u g h t h e ar c h i te c tu r e o f t h e m a c h i n e s u p p o r t i n g t h e p r o b l e m s o l v e r . M o s t o f th es e

s t u d i e s a r e c o n c e r n e d w i t h d e v i c e s l i k e p r o d u c t i o n o r d e r i n g , r ec enc y c r i t e r i a f o r w o r k i n g

m e m o r y e l e m e n t s , an d p r i o r i t y m ea s ur es o n p r o d u c t i o n s a n d m e m o r y e l e m e n t s . [ H a y e s -R o t h

and L e s s e r 1 9 7 7 , M c D e r m o t t a n d F o r g y 1 9 7 6 ]

Drew M c D e r m o t t s [ 1 9 7 6 ] NASL i n t e r p r e t e r e x p l i c i t l y r e c o r d s c o n t r o l as s er ti on s i n

g u i d i n g a n e l e c t r o n i c c i r c u i t d e s i g n p r o g r a m . His s ys te m a l s o r e c o r d s s o m e d e p e n d e n c y


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information, butd o e s s o I n a n a u t o m a t i c f a s h i o n r at h er t h a n e x p l i c i t l y . Other u s es o fe x p l i c i t representations of the problem solver control s ta te ar eu s ed in NOAH [Sacerdot i1 9 7 5 ] and MYCIN [Davis 1 9 7 6 ] . Product ion S y s t em problem solvers (such a s GPSR[ R y c h n e r 1 9 7 6 ] ) n e c e s s a r I l y r e c o r d g o a l s e x p l i c i t l y i n w o r k i n g m e m o r y , b u t o n l y a s an

i m p l e m e n t a t i o n o f s ta nd ar d c o n s e q u e n t r e a s o n i n g , r a t h e r t h a n a s a mechanism f o r c a r e f u l

c o n t r o l .

Well-Founded Suppor tM e a n s f o r e f f e c t i v e l y m a i n t a i n i n g a w e l l - f o u n d e d j u s t i f i c a t i o n f o r e a c h b e l i e v e d

f a c t have b e e n i n v e s t i g a t e d b y D o y l e [1 9 77 1 His s ys t e m TMS (Truth M a i n t e n a n c e Syst em)

h a s been i nc or p or ate d i n o ur d e s i g n o f AMORD.

B a c k t r a c k i n g

D e p e n d e n c y - D i r e c t e d Ba c k t r a c k i ng i s a t e c h n i q u e for careful backtracking whichwa s i nt r od uc ed b y St al l m an a n d S u s s m a n [ 1 9 7 6 ) in th e contexto f electrical circuitanalysis.

S e p a r a t i o n

Hayes ( 1 9 7 3 ] , K o w a l s k i [ 1 9 7 4 ] , a n d P r a t t [ 1 9 7 7 ] h a v e advocated th e separation ofp r o b l e m s o l v i n g k n o w l e d g e i n t o c o m p e t e n c e a n d p er for m an c e c o m p o n e n t s . We f e e l t h a t

t h i s i s t h e w r o n g d i s t i n c t i o n t o m a k e , a s t h e c o m p e t e n c e knowledge m ust necessari ly b er e p l i c a t e d i n t h e p e r f o r m a n c e k n o w l e d g e . Our p r o p o s e d m e t h o d o l o g y r e q u i r e s t h e s e f o r m s

o f k now ledge t o b e i n t e g r a t e d f o r e f f i c i e n t c o n t r o l , b u t s e p a r a t e d b y e x p l i c i t l y r e c o r d e d

d e p e n d e n c i e s .

Micro-PLANNERMicro-PLANNER [Sussman, W inograd,a nd Charniak 1 9 7 0 ] w as a language

based o n H e w i t t s [ 1 9 7 2 ) PLANNER w h i c h h a d a p e r v a s i v e s y s t e m o f c h r o n o l o g i c a lbacktracking.

C o n t r o l V o c a b u l a r y

McDermott [1977]argues that it i s t h e v o c a b u l a r y u s e d i n e x p l i c i t ( p r o d u c t i o n - l i k e )control that is important,not the specific machine architecture. S ee a l s o th e detailedvocabularies h e CMcDermot t 1 9 7 6 )and Sacerdoti [ 1 9 7 5 ]develop for talking abou t tasks anda c t i o n s .

S u p p r e s s i o n

Of c o u r s e , r e d u n d a n t c o n j u n c t s c a n b e s u p p r e s s e d b y b u i l d i n g t h e s em an t i c s o f

conjunction into th e problem solver. This justputs offthe problem a s non-primitiverelations ca n also explode in thisfashion. Resolution [Robinson 1 9 6 5 ] and associatedc o m b i n a t o r i a l s t r a t e g i e s ar e domain I nd ep en d en t techniques for suppressing so m ec o m b i n a t o r i a l e x p l o s i o n s w h i l e m a i n t a i n i n g c o m p l e t e n e s s .


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de Kleer, Doyle, S tee le & Sussman 2 0 Explicit Control of Reasoning

I m p li c a ti o n sIt is sometimes n e ce s sa r y to der ive a n i m p l i c a t i o n a s a subgoal, a s in a c o n d i t i o n a l

proof in natural d eduction. In thisexample w e have not provided for such subgoals. Thedetailsof conditional proof in the context of a truth maintenance s y s t em ar e descr ibed byD o y l e [ 1 9 7 7 ] .

AMORD

A M i r ac l e o f Rare D e v i c e , a n a m e t a k e n f r o m S . T . C o l e r i d g e s K u bl a K h an .

AMORD h a s b e e n i m p l e m e n t e d i n SCHEME [ S u s s m a n a n d S t e e l e 1 9 7 5 ] , a l e x i c a l l y - s c o p e d

dialectof LISP with tail recursion.

V a r i a n t s

I n AMORD, f a c t s a r e i nd exe d s o t h a t v a r i a n t s t a t e m e n t s o f a f a c t a r e i d e n t i f i e d .

If a f a c t i s d e r i v e d in different w ays , it is justified by e a c h o f t h e v a r i o u s d e r i v a t i o n s .These multiple justifications are useful ifa d er ivation is later withdrawn. [Sta l lman and

Sussman 1 9 7 6 , Doy le 1 9 7 7 )

U n i f i e s

Ourm atcher is b a s e d o n t h e u n i f i c a t i o n a l g o r i t h m u s ed in resolution, but ignoresthe restrictionso f first order logic. In particular,there a re no dist inguished symbols orpositions.

O r d e r

Th e AMORD language d oe s not specify theorder in which rules are executed.The order is irrelevant to th ediscussion in the text.

NogoodA s u m m ar y of th e r e a so n s for a contradict ion which ar e independent of a

p a r t i c u l a r s e t o f a s s um p t i o n s i s u s e d i n ARS[ S t a l l m a n a n d S u s s m a n 1 9 7 6 ) t o r e s t r i c t f u t u r e

c h oi c es . Doyle [ 1 9 7 7 ) extended a n d c l a r i f i e d t h i s n o t i o n a n d i t s r e l a t i o n s h i p t o t h e l o g i c a l

n o t i o n o f c o n d i t i o n a l p r o o f .

S i t u a t i o n s

The s i t u a t i o n a l c a l c u l u s fo r m al i z at i on s o f c h a n g i n g w o r l d wa s i n t r o d u c e d b y

McCarthy [1 9 68 ), and further developed by McCar thy and Hayes [ 1 969 ) . This t e c h n i q u e i sclosely related to th e methods of moda l logic. [Kripke 1 9 6 3 )

ConstructionGreens [1 9 6 9 ] method of constructive proof d id no ttake into account th e initial

situation. For example, on e should s ta te the g o a l : (EXISTS (S ) (AND (FU TU RE INIT 5)(TR U E (O N A B ) S))) where F U T U R E I s def ined according to th eoperators that are

applicable.


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S u b g o a l F i l t e r s

S o me impossible subgoals ca n b e p r u n e d by usinga n external sem antic filter.G e l e r n t e r s [ 1 9 6 3 ] G e o m e t r y M a c h i n e u s es a n a n a l y t i c g e o m e t r y d i a g r a m f o r t h i s p u r p o s e .

I s l a n d sTh e c o n c e p t o f r e f i n e m e n t p l an ni ng with islands w as i n t r o d u c e d b y Minsky

[ 1 9 6 3 ] .

H i g h e r S p a c e B CRefinement planning might b e viewed from the GPS [Ernst an d Newel l 1 9 6 9 ) and

ABSTRIPS [Sacerdotl 1 9 7 4 ] p erspective a s backward chaining in a higher level spacewhich controls the activities in th e action s equence space .

Equivalent GoalsWe mean equivalences relative to situational variables. There are other types of

equivalences which ar e not caught by thistechnique, s u c h a s that between th e goals ( A N O AB ) and (A ND B A ).

PCBG

One wa y I n w h i c h a s o l u t i o n o f a c o n j u n c t i o n b y a l i n e a r p l a n m a y b e i n c o r r e c t i s

t h e P r e r e q u i s i t e - C l o b b e r s - B r o t h e r - G o a l bu g d i s c u s s e d b y S u s s m a n [ 1 9 7 4 , 1 9 7 5 ) . This b u g

may be fi x ed b y r e o r d e r i n g t h e p l a n . O t h e r r e l a t e d b u g s i n t h e w o r l d o f f i x e d - i n s t r u c t i o n

t u r t l e programs a r e d i s c u s s e d b y G o l d s t e i n [ 1 9 7 4 ) .

A n o m a l o u sA l l e n B r o w n [ S u s s m a n 1 9 7 5 ) d i s c o v e r e d t h a t i t i s i m p o s s i b l e t o u s e a l i n e a r p l a n t o

c o n s t r u c t ( A N O (O N A B ) ( ON B C ) ) i f t h e I n i t i a l s i t u a t i o n c o n t a i n s ( ON C A ) . T a t e

[ 1 9 7 4 ] , Sa c er d ot i [ 1 9 7 5 ] , an d W arren [ 1 9 7 4 ) h a v e p r o p o s e d s e v e r a l s o l u t i o n s t o t h i s p r o b l e m .


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B i b l i o g r a p h y

[ D a v i s 1 9 7 6 ]

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a n d Us e o f L a r g e Know ledge B a s e s , Stanford A L L ab Me m o AIM-283, July 1 9 7 6 .

[D o yl e 1 9 7 7 ]

J o n D o y l e , T r u t h M a i n t e n a n c e S y s t e m s f o r P r o b l e m S o l v i n g , MIT A L L a b T R - 4 1 9 , 1 9 7 7 .

[ E r n s t a n d N e w e l l 1 9 6 9 ]G e o r g e W . Ernst and Allen Newell, OPS:A Case Study inGenerality and Problem-Solving,

A c a d e m i c P r e s s , Ne w Yo r k , 1 9 6 9 .

[ G e l e r n t e r 1 9 6 3 ]H. G e l e r n t e r , R e a l i z a t i o n o f a G e o m e t r y - T h e o r e m P r o v i n g M a c h i n e , i n F eigenbaum a n d

Feldman, Computers and Thought, pp . 1 3 4 - 1 5 2 .

[ G o l d s t e i n 1 9 7 4 ]

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Systems, in Mel tzer an d M i c h i e , Machine IntellIgence 4,p p . 1 8 3 - 2 0 5 .

[ H a y e s 1 9 7 3 ]

P . J . Hayes, Computation a n d D e d u c t i o n , P r o c . M F C S , 1 9 7 3 .

[Hayes-Roth and Lesser 1 9 7 7 ]F . Hayes-Roth an d V . R . L e s s e r , F o c u s o f A t t e n t i o n i n t h e H e a r s a y - I L S p e e c h

Understanding System, CM U CS report, January 1 9 7 7 .

[ H e w i t t 1 9 7 2 ]

C a r l E . H e w i t t , D e s c r i p t i o n a n d T h e o r e t i c a l A n a l y s i s ( U s i n g S c h e m a t a ) o f PLANNER: A

L a n g u a g e f o r P r o v i n g Theorems a n d M a n i p u l a t i n g M o d e l s i n a R o b o t , MIT Al L a b ,

T R - 2 5 8 , A p r i l 1 9 7 2 .

[ H e w i t t 1 9 7 5 )

C a r l H e w i t t , How t o U s e What Y o u K n o w , 1JCAI 4 , S e p t e m b e r 1 9 7 5 , p p . 1 8 9 - 1 9 8 .


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de Kleer, Doyle, S tee le & S u s s m a n 2 3 E x p l i c i t C on tr ol o f R e a s o n i n g

[ K o w a i s k i 1 9 7 4 ]

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Computational Logic, DC L M e m o 75 , 1 9 7 4 .

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1 9 6 3 .

[McCarthy 1 9 6 8 ]John M c C a r t h y , P r o g r a m s W i t h Common S e n s e , i n M i n s k y , Semantic Information

Processing, p p . 4 0 3 - 4 1 8 .

[McCarthy a nd Hayes 1 9 6 9 ]

J . McCarthy and P . J . H a y e s , S o m e P h i l o s o p h i c a l Problems from th e Standpoint ofArtificial Intelligence, in Mel tzer an d M i c h i e , Machine Intelligence 4 , p p . 4 6 3 - 5 0 2 .

[ M c D e r m o t t 1 9 7 6 ]

Drew Vincent McDermott, Flexibility an d Efficiency in a Com puter Program forDesigning Circuits, MITA! Lab TR-402 , December 1 9 7 6 .

[McDermott 1 9 7 7 ]Drew McDermott, Vocabular ies for Problem Solver State Descriptions, I/CA 1 5, A u g u s t

1 9 7 7 .

[ M cD e rm ot t an d F o r g y 1 9 7 6 ]J . McDermott an d C . F o r g y , P r o d u c t i o n S y s t e m C o n f l i c t R e s o l u t i o n S t r a t e g i e s , CMU CSr e p o r t , December 1 9 7 6 .

[Minsky 1 9 6 3 )M a r v i n L . M i n s k y , S t e p s T o w a r d A r t i f i c i a l I n t e l l i g e n c e , i n Feigenbaum an d F e l d m a n ,

Computers and Thought, pp . 4 06 -4 50 .

[Minsky 1 9 7 7 )

M a r v i n L . M i n s k y , P l a i n Talkabout NeurodevelopmentalEpistemology, 1/CAl 5, August1 9 7 7 .

[ N e w e l l a n d S i m o n 1 9 7 2 ]A l l e n N e w e l l an d H e r b e r t S i m o n , Human ProblemSolving, P rentice-Hal l , Englewood Cliffs,

NJ, 1 9 7 2 .

[Pratt 1 9 7 7 )Vaughan R . Pratt, The CompetencelPerformance D ichotomy in Programming, MIT AL

Lab M e m o 4 0 0 , January 1 9 7 7 .


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[Robinson 1 9 65 )J . A . R o b i n s o n , A M a c h i n e - O r i e n t e d L o g i c B a s e d o n t h e R e s o l u t i o n P r i n c i p l e , JACM, 12

(January 1 9 6 5 ) , p p . 2 3 - 4 1 .

[Rychner 1 9 7 6 )M i c h a e l D . Rychner, P r o d u c t i o n S y s t e m s a s a P r o g r a m m i n g L a n g u a g e f o r A r t i f i c i a l

Intelligence A ppl ications, CMU CS Report , December 1 9 7 6 .

[ S a c e r d o t i 1 9 7 4 )

Ea r l D . S a c e r d o t i , P l a n n i n g i n a Hi er ar c h y o f A b s t r a c t i o n S p a c e s , Artificial Intelligence,

V o l . 5 , N o . 2 , p p . 1 1 5 - 1 3 5 .

[Sacerdoti 1 9 7 5 ]Earl D. Sacerdoti, A Structure for P lans and Behavior , S R I Al Center, TN1 0 9 , August

1 9 7 5 .

[Simon 1 9 6 9 ]Herbert Simon,The Sciences ofthe Artificial, MIT P r e s s , Cam br idge, Massachusetts, 1 9 6 9 .

[Stallman and Sussman 1 9 7 6 )Richard M. Stallman and Gerald Ja y S uss m an , Forward R e a s o n i n g an d D e p e n d e n c y -

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