Logic Programming and Knowledge Representation

Abstract In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider extensions of the language of definite logic programs by classical (strong) negation, disjunction, and some modal operators and show how each of the added features extends the representational power of the language. We also discuss extensions of logic programming allowing abductive reasoning, meta-reasoning and reasoning in open domains. We investigate the methodology of using these languages for representing various forms of nonmonotonic reasoning and for describing knowledge in specific domains. We also address recent work on properties of programs needed for successful applications of this methodology such as consistency, categoricity and complexity.

[1]  José Júlio Alferes,et al.  Well Founded Semantics for Logic Programs with Explicit Negation , 1992, ECAI.

[2]  Paolo Mancarella,et al.  Generalized Stable Models: A Semantics for Abduction , 1990, ECAI.

[3]  Drew McDermott,et al.  Nonmonotonic Logic II: Nonmonotonic Modal Theories , 1982, JACM.

[4]  José Júlio Alferes,et al.  Default Theory for Well Founded Semantics with Explicit Negation , 1992, JELIA.

[5]  Michael Gelfond,et al.  Logic Programs with Classical Negation , 1990, ICLP.

[6]  Phan Minh Dung,et al.  On the Relations between Stable and Well-Founded Semantics of Logic Programs , 1992, Theor. Comput. Sci..

[7]  Teodor C. Przymusinski Three-Valued Formalizations of Non-Monotonic Reasoning and Logic Programming , 1989, KR.

[8]  Drew McDermott,et al.  Nonmonotonic Logic and Temporal Projection , 1987, Artif. Intell..

[9]  Klaus W. Wagner,et al.  Bounded Query Classes , 1990, SIAM J. Comput..

[10]  Drew McDermott,et al.  Non-Monotonic Logic I , 1987, Artif. Intell..

[11]  Robert A. Kowalski,et al.  Abduction Compared with Negation by Failure , 1989, ICLP.

[12]  Raymond Reiter,et al.  A Logic for Default Reasoning , 1987, Artif. Intell..

[13]  José Júlio Alferes,et al.  Optative Reasoning with Scenario Semantics , 1993, ICLP.

[14]  Donald W. Loveland,et al.  A Simple Near-Horn Prolog Interpreter , 1988, ICLP/SLP.

[15]  John McCarthy,et al.  Programs with common sense , 1960 .

[16]  Phan Minh Dung,et al.  Representing Actions in Logic Programming and Its Applications in Database Updates , 1993, ICLP.

[17]  Raymond Reiter,et al.  Equality and Domain Closure in First-Order Databases , 1980, JACM.

[18]  Christine Froidevaux,et al.  General Logical Databases and Programs: Default Logic Semantics and Stratification , 1991, Inf. Comput..

[19]  Raymond Reiter,et al.  A Logical Framework for Depiction and Image Interpretation , 1989, Artif. Intell..

[20]  McDermottDrew Nonmonotonic Logic II , 1982 .

[21]  Chitta Baral Issues in knowledge representation: semantics and knowledge combination , 1992 .

[22]  Georg Gottlob,et al.  Complexity Results for Disjunctive Logic Programming and Application to Nonmonotonic Logics , 1993, ILPS.

[23]  Kurt Konolige,et al.  Computing the Extensions of Autoepistemic and Default Logics with a Truth Maintenance System , 1990, AAAI.

[24]  Robert A. Kowalski,et al.  Problems and Promises of Computational Logic , 1990 .

[25]  Michael Kifer,et al.  HILOG: A Foundation for Higher-Order Logic Programming , 1993, J. Log. Program..

[26]  David Poole,et al.  What the Lottery Paradox Tells Us About Default Reasoning , 1989, KR.

[27]  Divesh Srivastava,et al.  The valid model semantics for logic programs , 1992, PODS '92.

[28]  Michael Gelfond,et al.  Representing Action and Change by Logic Programs , 1993, J. Log. Program..

[29]  Hiroshi Fujita,et al.  A Model Generation Theorem Prover in KL1 Using a Ramified -Stack Algorithm , 1991, International Conference on Logic Programming.

[30]  David S. Warren,et al.  Representing actions in logic programming and its applications in database updates , 1993 .

[31]  Robert C. Moore Semantical Considerations on Nonmonotonic Logic , 1985, IJCAI.

[32]  Kave Eshghi,et al.  Computing Stable Models by Using the ATMS , 1990, AAAI.

[33]  Miroslaw Truszczynski,et al.  Nonmonotonic Reasoning is Sometimes Simpler , 1993, Kurt Gödel Colloquium.

[34]  Randy Goebel,et al.  Theorist: A Logical Reasoning System for Defaults and Diagnosis , 1987 .

[35]  Raymond Reiter,et al.  Temporal Reasoning in Logic Programming: A Case for the Situation Calculus , 1993, ICLP.

[36]  Anil Nerode,et al.  Computation and implementation of non-monotonic deductive databases , 1991 .

[37]  Liz Sonenberg,et al.  On Domain Independent Databases , 1988, Foundations of Deductive Databases and Logic Programming..

[38]  Cees Witteveen,et al.  Skeptical reason belief revision maintenance and , 2002 .

[39]  Vladimir Lifschitz,et al.  On the Declarative Semantics of Logic Programs with Negation , 1987, Foundations of Deductive Databases and Logic Programming..

[40]  Melvin Fitting Well-Founded Semantics, Generalized , 1991, ISLP.

[41]  Pietro Torasso,et al.  On the Relationship between Abduction and Deduction , 1991, J. Log. Comput..

[42]  Teodor C. Przymusinski On the Declarative Semantics of Deductive Databases and Logic Programs , 1988, Foundations of Deductive Databases and Logic Programming..

[43]  Allen Van Gelder,et al.  Negation as Failure using Tight Derivations for General Logic Programs , 1988, J. Log. Program..

[44]  Gerd Wagner Reasoning with Inconsistency in Extended Deductive Databases , 1993, LPNMR.

[45]  Sarit Kraus,et al.  Nonmonotonicity and the Scope of Reasoning , 1991, Artif. Intell..

[46]  Michael J. Maher,et al.  Foundations of Deductive Databases and Logic Programming , 1988 .

[47]  Kenneth A. Ross,et al.  The well-founded semantics for general logic programs , 1991, JACM.

[48]  José Júlio Alferes,et al.  On Logic Program Semantics with Two Kinds of Negation , 1992, JICSLP.

[49]  Antonio Brogi,et al.  Meta for Modularising Logic Programming , 1992, META.

[50]  Carlo Zaniolo,et al.  Stable models and non-determinism in logic programs with negation , 1990, PODS.

[51]  J. Lloyd Foundations of Logic Programming , 1984, Symbolic Computation.

[52]  Melvin Fitting Partial Models and Logic Programming , 1986, Theor. Comput. Sci..

[53]  Kenneth A. Ross,et al.  A procedural semantics for well founded negation in logic programs , 1989, J. Log. Program..

[54]  Phan Minh Dung,et al.  Negations as Hypotheses: An Abductive Foundation for Logic Programming , 1991, ICLP.

[55]  Teodor C. Przymusinski The Well-Founded Semantics Coincides with the Three-Valued Stable Semantics , 1990, Fundam. Inform..

[56]  Marco Schaerf,et al.  A Survey of Complexity Results for Nonmonotonic Logics , 1993, J. Log. Program..

[57]  Daniel Lehmann,et al.  What does a Conditional Knowledge Base Entail? , 1989, Artif. Intell..

[58]  Teodor C. Przymusinski,et al.  Stationary Default Extensions , 1994, Fundam. Informaticae.

[59]  Jack Minker,et al.  An Extension to Linear Resolution with Selection Function , 1982, Inf. Process. Lett..

[60]  Teodor C. Przymusinski,et al.  The extended closed world assumption and its relationship to parallel circumscription , 1985, PODS '86.

[61]  Murray Shanahan,et al.  Prediction is Deduction but Explanation is Abduction , 1989, IJCAI.

[62]  Edward P. F. Chan A Possible World Semantics for Disjunctive Databases , 1993, IEEE Trans. Knowl. Data Eng..

[63]  Danny De Schreye,et al.  A Perfect Herbrand Semantics for Untyped Vanilla Meta-Programming , 1992, JICSLP.

[64]  Teodor C. Przymusinski Stationary Semantics for Disjunctive Logic Programs and Deductive Databases , 1990, NACLP.

[65]  John L. Cuadrado,et al.  A Truth Maintenance System Based on Stable Models , 1989, NACLP.

[66]  Hisao Tamaki,et al.  Unfold/Fold Transformation of Logic Programs , 1984, ICLP.

[67]  Alan Mycroft,et al.  Logic Programs and Many-Valued Logic , 1984, STACS.

[68]  Michael Gelfond,et al.  Negation as Failure: Careful Closure Procedure , 1986, Artif. Intell..

[69]  Charles S. Peirce,et al.  Elements of logic , 1960 .

[70]  Adrian Walker,et al.  Towards a Theory of Declarative Knowledge , 1988, Foundations of Deductive Databases and Logic Programming..

[71]  Robert A. Kowalski,et al.  Logic for problem solving , 1982, The computer science library : Artificial intelligence series.

[72]  Robert A. Kowalski,et al.  A Metalogic Programming Approach to Multi-Agent Knowledge and Belief , 1991, Artificial and Mathematical Theory of Computation.

[73]  Michael Gelfond,et al.  Reasoning on Open Domains , 1993, LPNMR.

[74]  Carolina Ruiz,et al.  On Extended Disjunctive Logic Programs , 1993, ISMIS.

[75]  Teodor C. Przymusinski Extended Stable Semantics for Normal and Disjunctive Programs , 1990, ICLP.

[76]  Kenneth Kunen,et al.  Negation in Logic Programming , 1987, J. Log. Program..

[77]  Dov M. Gabbay,et al.  Theoretical Foundations for Non-Monotonic Reasoning in Expert Systems , 1989, Logics and Models of Concurrent Systems.

[78]  Chitta Baral,et al.  Representing Concurrent Actions in Extended Logic Programming , 1993, IJCAI.

[79]  W. V. Quine,et al.  Collected Papers of Charles Sanders Peirce.-- Volume III: Exact Logic. Charles Sanders Peirce , Charles Hartshorne , Paul Weiss , 1934 .

[80]  Georg Gottlob,et al.  Complexity Results for Nonmonotonic Logics , 1992, J. Log. Comput..

[81]  Teodor C. Przymusinski Perfect Model Semantics , 1988, ICLP/SLP.

[82]  David S. Touretzky,et al.  The Mathematics of Inheritance Systems , 1984 .

[83]  Georg Gottlob,et al.  Complexity aspects of various semantics for disjunctive databases , 1993, PODS '93.

[84]  Jack Minker,et al.  Bottom-Up Evaluation of Hierarchical Disjunctive Deductive Databases , 1991, ICLP.

[85]  Ken Satoh,et al.  Computing Abduction by Using the TMS , 1991, ICLP.

[86]  Katsumi Inoue Studies on abductive and nonmonotonic reasoning , 1993 .

[87]  L. Thorne McCarty,et al.  Adding Negation-as-Failure to Intuitionistic Logic Programming , 1990, NACLP.

[88]  Christos H. Papadimitriou,et al.  Why not negation by fixpoint? , 1988, PODS '88.

[89]  Michael Gelfond,et al.  Autoepistemic Logic and Formalization of Commonsense Reasoning: Preliminary Report , 1988, NMR.

[90]  Jürgen Dix,et al.  Classifying Semantics of Disjunctive Logic Programs , 1992, JICSLP.

[91]  Georg Gottlob,et al.  Expressive Power and Complexity of Disjunctive Datalog under the Stable Model Semantics , 1994, IS/KI.

[92]  Paolo Mancarella,et al.  Stable Theories for Logic Programs , 1991, ISLP.

[93]  Raymond Reiter,et al.  A Theory of Diagnosis from First Principles , 1986, Artif. Intell..

[94]  Joseph R. Shoenfield,et al.  Mathematical logic , 1967 .

[95]  Harvey Abramson,et al.  Meta-programming in logic programming , 1989 .

[96]  Lawrence Cavedon,et al.  Continuity, Consistency, and Completeness Properties for Logic Programs , 1989, ICLP.

[97]  Fangzhen Lin A study of nonmonotonic reasoning , 1992 .

[98]  Jack Minker,et al.  An Overview of Nonmonotonic Reasoning and Logic Programming , 1993, J. Log. Program..

[99]  Katsumi Inoue,et al.  Embedding Negation as Failure into a Model Generation Theorem Prover , 1992, CADE.

[100]  José Júlio Alferes,et al.  Non-Monotonic Reasoning with Logic Programming , 1993, J. Log. Program..

[101]  François Bry,et al.  SATCHMO: A Theorem Prover Implemented in Prolog , 1988, CADE.

[102]  Vladimir Lifschitz,et al.  Answer Sets in General Nonmonotonic Reasoning (Preliminary Report) , 1992, KR.

[103]  Vladimir Lifschitz,et al.  Computing Circumscription , 1985, IJCAI.

[104]  Georg Gottlob,et al.  Propositional Circumscription and Extended Closed-World Reasoning are IIp2-Complete , 1993, Theor. Comput. Sci..

[105]  Laura Giordano,et al.  Negation as Failure in Intuitionistic Logic Programming , 1992, JICSLP.

[106]  Maurice Bruynooghe,et al.  Temporal Reasoning with Abductive Event Calculus , 1992, ECAI.

[107]  Jianhua Chen Minimal Knowledge + Negation as Failure = Only Knowing (Sometimes) , 1993, LPNMR.

[108]  K. Apt Fundamenta informaticae on Logic Programming , 1990 .

[109]  Anil Nerode,et al.  Logic programming and non-monotonic reasoning : proceedings of the second international workshop , 1991 .

[110]  David Poole,et al.  A Logical Framework for Default Reasoning , 1988, Artif. Intell..

[111]  David Scott Warren,et al.  Query evaluation under the well-founded semantics , 1993, PODS.

[112]  John S. Schlipf,et al.  The Expressive Powers of the Logic Programming Semantics , 1995, J. Comput. Syst. Sci..

[113]  Vladimir Lifschitz,et al.  Extended Logic Programs as Autoepistemic Theories , 1993, LPNMR.

[114]  Chitta Baral,et al.  Generalized Negation As Failure and Semantics of Normal Disjunctive Logic Programs , 1992, LPAR.

[115]  John McCarthy,et al.  SOME PHILOSOPHICAL PROBLEMS FROM THE STANDPOINT OF ARTI CIAL INTELLIGENCE , 1987 .

[116]  Chris Evans,et al.  Negation-as-failure as an approach to the Hanks-McDermott problem , 1989 .

[117]  Raymond Reiter,et al.  Circumscription Implies Predicate Completion (Sometimes) , 1982, AAAI.

[118]  David Nelson,et al.  Constructible falsity , 1949, Journal of Symbolic Logic.

[119]  Charles Elkan,et al.  A Rational Reconstruction of Nonmonotonic Truth Maintenance Systems , 1990, Artif. Intell..

[120]  David Harel,et al.  Horn Clauses Queries and Generalizations , 1985, J. Log. Program..

[121]  Danny De Schreye,et al.  Representing Incomplete Knowledge in Abductive Logic Programming , 1993, J. Log. Comput..

[122]  William L. Rodi,et al.  A Nonmonotonic Assumption-Based TMS Using Stable Bases , 1991, KR.

[123]  Fangzhen Lin,et al.  A Logic of Knowledge and Justified Assumptions , 1992, Artif. Intell..

[124]  Teodor C. Przymusinski,et al.  Semantic Issues in Deductive Databases and Logic Programs , 1990 .

[125]  Jack Minker,et al.  Disjunctive Deductive Databases , 1992, LPAR.

[126]  Peter J. Stuckey,et al.  Semantics of Logic Programs with Aggregates , 1991, ISLP.

[127]  John McCarthy,et al.  Circumscription - A Form of Non-Monotonic Reasoning , 1980, Artif. Intell..

[128]  Robert A. Kowalski,et al.  Amalgamating language and metalanguage in logic programming , 1982 .

[129]  José Júlio Alferes,et al.  Contradiction Removal within Well Founded Semantics , 1991, LPNMR.

[130]  Gaetano Aurelio Lanzarone,et al.  A Metalogic Programming Language , 1989, ICLP.

[131]  Georg Gottlob,et al.  The complexity of logic-based abduction , 1993, JACM.

[132]  Fangzhen Lin,et al.  Argument Systems: A Uniform Basis for Nonmonotonic Reasoning , 1989, KR.

[133]  Jia-Huai You,et al.  Making default inferences from logic programs , 1991, Comput. Intell..

[134]  Grigori Schwarz Autoepistemic Logic of Knowledge , 1991, LPNMR.

[135]  Victor W. Marek,et al.  The Relationship Between Logic Program Semantics and Non-Monotonic Reasoning , 1989, ICLP.

[136]  John W. Lloyd,et al.  The Godel Report , 1991 .

[137]  Michael Gelfond,et al.  Representing Null Values in Logic Programming , 1994, LFCS.

[138]  Paul H. Morris,et al.  The Anomalous Extension Problem in Default Reasoning , 1988, Artif. Intell..

[139]  Jack Minker,et al.  On Indefinite Databases and the Closed World Assumption , 1987, CADE.

[140]  Michael Gelfond,et al.  On Stratified Autoepistemic Theories , 1987, AAAI.

[141]  Dale Miller,et al.  A Theory of Modules for Logic Programming , 1986, SLP.

[142]  Teodor C. Przymusinski,et al.  Weakly Perfect Model Semantics for Logic Programs , 1988, ICLP/SLP.

[143]  Ken Satoh,et al.  A Correct Goal-directed Proof Procedure for a General Logic Program with Integrity Constraints , 1992, ELP.

[144]  Kenneth Kunen,et al.  Signed Data Dependencies in Logic Programs , 1989, J. Log. Program..

[145]  Vladimir Lifschitz,et al.  Between Circumscription and Autoepistemic Logic , 1989, KR.

[146]  Chiaki Sakama,et al.  Possible Model Semantics for Disjunctive Databases , 1989, DOOD.

[147]  Danny De Schreye,et al.  Why untyped non-ground meta-programming is not (much of) of problem , 1992 .

[148]  H. Przymusinska,et al.  Weakly stratified logic programs , 1990 .

[149]  Michael J. Maher,et al.  Optimal Fixedpoints of Logic Programs , 1985, Theor. Comput. Sci..

[150]  Gerd Wagner,et al.  Logic Programming with Strong Negation and Inexact Predicates , 1991, J. Log. Comput..

[151]  Maurizio Lenzerini,et al.  The Complexity of Closed World Reasoning and Circumscription , 1990, AAAI.

[152]  Melvin Fitting,et al.  Stratified and Three-valued Logic Programming Semantics , 1988, ICLP/SLP.

[153]  Matthew L. Ginsberg,et al.  Readings in Nonmonotonic Reasoning , 1987, AAAI 1987.

[154]  Michael Gelfond,et al.  Formalization of inheritance reasoning in autoepistemic logic , 1990 .

[155]  John McCarthy,et al.  Applications of Circumscription to Formalizing Common Sense Knowledge , 1987, NMR.

[156]  Allen Van Gelder,et al.  The Alternating Fixpoint of Logic Programs with Negation , 1993, J. Comput. Syst. Sci..

[157]  Robert A. Kowalski,et al.  The Semantics of Predicate Logic as a Programming Language , 1976, JACM.

[158]  Jorge Lobo,et al.  Foundations of disjunctive logic programming , 1992, Logic Programming.

[159]  Jack Minker,et al.  A Fixpoint Semantics for Disjunctive Logic Programs , 1990, J. Log. Program..

[160]  Allen Van Gelder,et al.  The well-founded semantics of aggregation , 1992, PODS.

[161]  Phan Minh Dung,et al.  Well-Founded Reasoning with Classical Negation , 1991, LPNMR.

[162]  Jean H. Gallier,et al.  Linear-Time Algorithms for Testing the Satisfiability of Propositional Horn Formulae , 1984, J. Log. Program..

[163]  Pierre Siegel,et al.  Saturation, Nonmonotonic Reasoning and the Closed-World Assumption , 1985, Artif. Intell..

[164]  Teodor C. Przymusinski,et al.  On the relationship between CWA, minimal model, and minimal herbrand model semantics , 1990, Int. J. Intell. Syst..

[165]  Joxan Jaffar,et al.  Completeness of the Negation as Failure Rule , 1983, IJCAI.

[166]  Robert A. Kowalski,et al.  Predicate Logic as Programming Language , 1974, IFIP Congress.

[167]  Hudson Turner,et al.  A Monotonicity Theorem for Extended Logic Programs , 1993, ICLP.

[168]  Paolo Mancarella,et al.  Abductive Logic Programming , 1992, LPNMR.

[169]  Krzysztof R. Apt,et al.  Arithmetic classification of perfect models of stratified programs , 1991, Fundam. Informaticae.

[170]  Hajnal Andréka,et al.  The generalized completeness of Horn predicate-logic as a programming language , 1978, Acta Cybern..

[171]  Melvin Fitting,et al.  A Kripke-Kleene Semantics for Logic Programs , 1985, J. Log. Program..

[172]  Michael Gelfond,et al.  Definitions in Epistemic Specifications , 1991, LPNMR.

[173]  Jean-Marie Jacquet,et al.  Introduction to Logic Programming , 1993, ICLP Workshop on Construction of Logic Programs.

[174]  M. Gelfond,et al.  Disjunctive Defaults , 1991 .

[175]  Patrick J. Hayes,et al.  Computation and Deduction , 1973, MFCS.

[176]  Philip T. Cox,et al.  Causes for Events: Their Computation and Applications , 1986, CADE.

[177]  Jon Doyle,et al.  A Truth Maintenance System , 1979, Artif. Intell..

[178]  François Fages,et al.  Consistency of Clark's completion and existence of stable models , 1992, Methods Log. Comput. Sci..

[179]  Vladimir Lifschitz,et al.  Closed-World Databases and Circumscription , 1987, Artif. Intell..

[180]  Judea Pearl,et al.  Embracing Causality in Formal Reasoning , 1987, AAAI.

[181]  Raymond Reiter On Closed World Data Bases , 1977, Logic and Data Bases.

[182]  Laura Giordano,et al.  Generalized Stable Models, Truth Maintenance and Conflict Resolution , 1990, ICLP.

[183]  Donald W. Loveland,et al.  Near-Horn PROLOG , 1987, ICLP.

[184]  Teodor C. Przymusinski,et al.  On the Relationship Between Circumscription and Negation as Failure , 1989, Artif. Intell..

[185]  José Júlio Alferes,et al.  Derivation Procedures for Extended Stable Models , 1991, IJCAI.

[186]  Phan Minh Dung,et al.  On the Acceptability of Arguments and its Fundamental Role in Nonmonotonic Reasoning and Logic Programming , 1993, IJCAI.

[187]  Kave Eshghi,et al.  Abductive Planning with Event Calculus , 1988, ICLP/SLP.

[188]  Teodor C. Przymusinski Every logic program has a natural stratification and an iterated least fixed point model , 1989, PODS.

[189]  Georg Gottlob,et al.  On the complexity of propositional knowledge base revision, updates, and counterfactuals , 1992, Artif. Intell..

[190]  Shinichi Honiden,et al.  Relating the TMS to Autoepistemic Logic , 1989, IJCAI.

[191]  Miroslaw Truszczynski,et al.  Reflexive autoepistemic logic and logic programming , 1993 .

[192]  Olga Kosheleva,et al.  Approximating General Logic Programs , 1993, ILPS.

[193]  Vladimir Lifschitz,et al.  On Open Defaults , 1990 .

[194]  Victor W. Marek,et al.  Autoepistemic logic , 1991, JACM.

[195]  Hisao Tamaki,et al.  OLD Resolution with Tabulation , 1986, ICLP.

[196]  Michael Gelfond,et al.  Representing Actions in Extended Logic Programming , 1992, JICSLP.

[197]  John McCarthy,et al.  Addendum: Circumscription and other Non-Monotonic Formalisms , 1980, Artif. Intell..