Integrating Inductive Definitions in SAT

We investigate techniques for supporting inductive definitions (IDs) in SAT, and report on an implementation, called MidL, of the resulting solver. This solver was first introduced in [11], as a part of a declarative problem solving framework. We go about our investigation by proposing a new formulation of the semantics of IDs as presented in [2]. This new formulation suggests a way to perform the computational task involved, resulting in an algorithm supporting IDs. We show in detail how to integrate our algorithm with traditional SAT solving techniques. We also point out the similarities with another algorithm that was recently developed for ASP [1]. Indeed, our formulation reveals a very tight relation with stable model semantics. We conclude by an experimental validation of our approach using MidL.

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

[2]  Luís Moniz Pereira,et al.  Computational Logic — CL 2000 , 2000, Lecture Notes in Computer Science.

[3]  Marc Denecker,et al.  Extending Classical Logic with Inductive Definitions , 2000, Computational Logic.

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

[5]  Johan Wittocx,et al.  MidL: A SAT(ID) solver , 2007 .

[6]  Frank Wolter,et al.  Monodic fragments of first-order temporal logics: 2000-2001 A.D , 2001, LPAR.

[7]  Johan Wittocx,et al.  The IDP framework for declarative problem solving , 2006 .

[8]  Martin Gebser,et al.  Approaching the core of unfounded sets , 2006 .

[9]  John S. Schlipf,et al.  Answer Set Programming with Clause Learning , 2004, LPNMR.

[10]  Krzysztof R. Apt,et al.  Logic Programming , 1990, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

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

[12]  Sharad Malik,et al.  Chaff: engineering an efficient SAT solver , 2001, Proceedings of the 38th Design Automation Conference (IEEE Cat. No.01CH37232).

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

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

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

[16]  Lawrence Ryan.  Efficient algorithms for clause-learning SAT solvers , 2004 .

[17]  Fangzhen Lin,et al.  ASSAT: computing answer sets of a logic program by SAT solvers , 2002, Artif. Intell..

[18]  Maurice Bruynooghe,et al.  Satisfiability Checking for PC(ID) , 2005, LPAR.

[19]  Martin Gebser,et al.  clasp : A Conflict-Driven Answer Set Solver , 2007, LPNMR.

[20]  Eugenia Ternovska,et al.  Reducing Inductive Definitions to Propositional Satisfiability , 2005, ICLP.

[21]  Alexander A. Razborov,et al.  Why are there so many loop formulas? , 2006, TOCL.

[22]  Yuliya Lierler,et al.  cmodels - SAT-Based Disjunctive Answer Set Solver , 2005, LPNMR.

[23]  Niklas Sörensson,et al.  An Extensible SAT-solver , 2003, SAT.