Fages' Theorem and Answer Set Programming

We generalize a theorem by Francois Fages that describes the relationship between the completion semantics and the answer set semantics for logic programs with negation as failure. The study of this relationship is important in connection with the emergence of answer set programming. Whenever the two semantics are equivalent, answer sets can be computed by a satisfiability solver, and the use of answer set solvers such as smodels and dlv is unnecessary. A logic programming representation of the blocks world due to Ilkka Niemelae is discussed as an example.

[1]  Danny De Schreye,et al.  Answer Set Planning , 1999 .

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

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

[4]  V. Lifschitz,et al.  Foundations of Logic Programming , 1997 .

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

[6]  Bart Selman,et al.  Planning as Satisfiability , 1992, ECAI.

[7]  Hantao Zhang,et al.  SATO: An Efficient Propositional Prover , 1997, CADE.

[8]  Vladimir Lifschitz,et al.  Representing Transition Systems by Logic Programs , 1999, LPNMR.

[9]  John W. Lloyd,et al.  Foundations of Logic Programming, 1st Edition , 1984 .

[10]  Victor W. Marek,et al.  Stable models and an alternative logic programming paradigm , 1998, The Logic Programming Paradigm.

[11]  Victor W. Marek,et al.  The Logic Programming Paradigm: A 25-Year Perspective , 2011 .