Credulous Resolution for Answer Set Programming

The paper presents a calculus based on resolution for credulous reasoning in Answer Set Programming. The new approach allows a top-down and goal directed resolution, in the same spirit as traditional SLD-resolution. The proposed credulous resolution can be used in query-answering with nonground queries and with non-ground, and possibly infinite, programs. Soundness and completeness results for the resolution procedure are proved for large classes of logic programs. The resolution procedure is also extended to handle some traditional syntactic extensions used in Answer Set Programming, such as choice rules and constraints. The paper also describes an initial implementation of a system for credulous reasoning in Answer Set Programming.

[1]  Tran Cao Son,et al.  Approximation of action theories and its application to conformant planning , 2005, Artif. Intell..

[2]  Fabio Massacci,et al.  Verifying security protocols as planning in logic programming , 2001, ACM Trans. Comput. Log..

[3]  Piero A. Bonatti,et al.  Reasoning with infinite stable models , 2001, Artif. Intell..

[4]  Michael Gelfond,et al.  The USA-Advisor: A Case Study in Answer Set Planning , 2001, LPNMR.

[5]  Ilkka Niemelä,et al.  Logic programs with stable model semantics as a constraint programming paradigm , 1999, Annals of Mathematics and Artificial Intelligence.

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

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

[8]  Timo Soininen,et al.  Extending and implementing the stable model semantics , 2000, Artif. Intell..

[9]  Joohyung Lee,et al.  A New Perspective on Stable Models , 2007, IJCAI.

[10]  Ilkka Niemelä,et al.  Bounded LTL model checking with stable models , 2001, Theory and Practice of Logic Programming.

[11]  Piero A. Bonatti.  Resolution for Skeptical Stable Model Semantics , 2004, Journal of Automated Reasoning.

[12]  V. S. Subrahmanian,et al.  Computing Non-Ground Representations of Stable Models , 1997, LPNMR.

[13]  Melvin Fitting.  Tableaux for logic programming , 2004, Journal of Automated Reasoning.

[14]  Martin Gebser,et al.  Tableau Calculi for Answer Set Programming , 2006, ICLP.

[15]  Agostino Dovier,et al.  An empirical study of constraint logic programming and answer set programming solutions of combinatorial problems , 2009, J. Exp. Theor. Artif. Intell..