The well-founded semantics for general logic programs

A general logic program (abbreviated to "program" hereafter) is a set of roles that have both positive and negative subgoals. It is common to view a deductive database as a general logic program consisting of rules (IDB) slttmg above elementary relations (EDB, facts). It is desirable to associate one Herbrand model with a program and think of that model as the "meaning of the program, " or Its "declarative semantics. " Ideally, queries directed to the program would be answered in accordance with this model. Recent research indicates that some programs do not have a "satisfactory" total model; for such programs, the question of an appropriate partial model arises. Unfounded sets and well-founded partial models are introduced and the well-founded semantics of a program are defined to be its well-founded partial model. If the well-founded partial model is m fact a total model. it is called the well-founded model. It n shown that the class of programs possessing a total well-founded model properly includes previously studied classes of "stratified" and "locally stratified" programs, The method in this paper is also compared with other proposals in the literature, including Clark's "program completion, " Fitting's and Kunen's 3-vahred interpretations of it, and the "stable models" of Gelfond and Lifschitz.

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

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

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

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

[5]  Kenneth A. Ross,et al.  Unfounded sets and well-founded semantics for general logic programs , 1988, PODS.

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

[7]  Drew McDermott,et al.  Default Reasoning, Nonmonotonic Logics, and the Frame Problem , 1986, AAAI.

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

[9]  John C. Shepherdson,et al.  Negation in Logic Programming , 1988, Foundations of Deductive Databases and Logic Programming..

[10]  John Wylie Lloyd,et al.  Foundations of Logic Programming , 1987, Symbolic Computation.

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

[12]  Moshe Y. Vardi.  The complexity of relational query languages (Extended Abstract) , 1982, STOC '82.

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

[14]  Allen Van Gelder,et al.  The Alternating Fixpoint of Logic Programs with Negation , 1989, J. Comput. Syst. Sci..

[15]  François Bry.  Logic Programming as Constructivism , 1989 .

[16]  Wiktor Marek,et al.  STABLE THEORIES IN AUTOEPISTEMIC LOGIC , 1989 .

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

[18]  Jeffrey D. Ullman,et al.  Design Overview of the NAIL! System , 1986, ICLP.

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

[20]  Allen Van Gelder,et al.  Modeling Simultaneous Events with Default Reasoning and Tight Derivations , 1990, J. Log. Program..

[21]  Kenneth Kunen.  Some Remarks on the Completed Database , 1988, ICLP/SLP.

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

[23]  Keith L. Clark,et al.  Negation as Failure , 1987, Logic and Data Bases.

[24]  J. W. Lloyd,et al.  Foundations of logic programming; (2nd extended ed.) , 1987 .

[25]  Y. Moschovakis.  Elementary induction on abstract structures (Studies in logic and the foundations of mathematics) , 1974 .

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

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

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

[29]  David Harel,et al.  Structure and Complexity of Relational Queries , 1980, FOCS.

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

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

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

[33]  Michael J. Maher.  Equivalences of Logic Programs , 1988, Foundations of Deductive Databases and Logic Programming..

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

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

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

[37]  Phan Minh Dung,et al.  A Natural Semantics for Logic Programs with Negation , 1989, FSTTCS.

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

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