Commonsense Axiomatizations for Logic Programs

Abstract Various semantics for logic programs with negation are described in terms of a dualized program together with additional axioms, some of which are second-order formulas. The semantics of Clark, Fitting, and Kunen are characterized in this framework, and a finite first-order presentation of Kunen's semantics is described. A new axiom to represent “commonsense” reasoning is proposed for logic programs. It is shown that the well-founded semantics and stable models are definable with this axiom. The roles of domain augmentation and domain closure are examined. A “domain foundation” axiom is proposed to replace the domain closure axiom.

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

[2]  Krishnaprasad Thirunarayan.  On the Computability of Circumscription , 1988, Inf. Process. Lett..

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

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

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

[6]  Kenneth Kunen,et al.  Some Remarks on the Completed Database , 1990, ICLP/SLP.

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

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

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

[10]  Serge Abiteboul,et al.  Procedural and declarative database update languages , 1988, PODS '88.

[11]  K. Jon Barwise,et al.  An introduction to recursively saturated and resplendent models , 1976, Journal of Symbolic Logic.

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

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

[14]  Donald Perlis,et al.  Computing Protected Circumscription , 1985, J. Log. Program..

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

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

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

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

[19]  Alan van Gelser.  Negation as failure using tight derivations for general logic programs , 1989 .

[20]  K. A. Ross.  Modular stratification and magic sets for DATALOG programs with negation , 1990, PODS 1990.

[21]  Vladimir Lifschitz,et al.  Pointwise Circumscription: Preliminary Report , 1986, AAAI.

[22]  Kenneth A. Ross,et al.  The Well Founded Semantics for Disjunctive Logic Programs , 1989, DOOD.

[23]  Krzysztof R. Apt,et al.  Contributions to the Theory of Logic Programming , 1982, JACM.

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

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

[26]  Kenneth A. Ross,et al.  Modular stratification and magic sets for Datalog programs with negation , 1994, JACM.

[27]  Haim Gaifman,et al.  Decidable optimization problems for database logic programs , 1988, STOC '88.

[28]  John C. Shepherdson,et al.  Negation as Failure II , 1985, J. Log. Program..

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

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

[31]  Jack Minker,et al.  A Stratification Semantics for General Disjunctive Programs , 1989, NACLP.

[32]  Saharon Shelah,et al.  Fixed-point extensions of first-order logic , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[33]  Christine Froidevaux,et al.  Negation by Default and Unstratifiable Logic Programs , 1991, Theor. Comput. Sci..

[34]  Neil Immerman,et al.  Relational Queries Computable in Polynomial Time , 1986, Inf. Control..

[35]  Peter Aczel,et al.  An Introduction to Inductive Definitions , 1977 .

[36]  Christos H. Papadimitriou,et al.  Some computational aspects of circumscription , 1988, JACM.

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

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

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

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

[41]  Van GelderAllen.  The alternating fixpoint of logic programs with negation , 1993 .

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

[43]  Yiannis N. Moschovakis,et al.  Elementary induction on abstract structures , 1974 .

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

[45]  J. W. LLOYD,et al.  Making Prolog more Expressive , 1984, J. Log. Program..

[46]  Daniel Leviant.  Inductive definitions over finite structures , 1990 .

[47]  Phokion G. Kolaitis.  The Expressive Power of Stratified Programs , 1991, Inf. Comput..