Conflict-Driven Disjunctive Answer Set Solving

We elaborate a uniform approach to computing answer sets of disjunctive logic programs based on state-of-the-art Boolean constraint solving techniques. Starting from a constraint-based characterization of answer sets, we develop advanced solving algorithms, featuring backjumping and conflict-driven learning using the First-UIP scheme as well as sophisticated unfounded set checking. As a final result, we obtain a competitive solver for ΣP2-complete problems, taking advantage of Boolean constraint solving technology without using any legacy solvers as black boxes.

[1]  Rina Dechter,et al.  Propositional semantics for disjunctive logic programs , 1994, Annals of Mathematics and Artificial Intelligence.

[2]  Sharad Malik,et al.  A Comparative Study of 2QBF Algorithms , 2004, SAT.

[3]  Martin Gebser,et al.  Conflict-Driven Answer Set Enumeration , 2007, LPNMR.

[4]  Gerald Pfeifer,et al.  Improving the Model Generation/Checking Interplay to Enhance the Evaluation of Disjunctive Programs , 2004, LPNMR.

[5]  Wolfgang Faber,et al.  The DLV system for knowledge representation and reasoning , 2002, TOCL.

[6]  Francesco Scarcello,et al.  Disjunctive Stable Models: Unfounded Sets, Fixpoint Semantics, and Computation , 1997, Inf. Comput..

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

[8]  David G. Mitchell,et al.  A SAT Solver Primer , 2005, Bull. EATCS.

[9]  Sharad Malik,et al.  Efficient conflict driven learning in a Boolean satisfiability solver , 2001, IEEE/ACM International Conference on Computer Aided Design. ICCAD 2001. IEEE/ACM Digest of Technical Papers (Cat. No.01CH37281).

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

[11]  Esra Erdem,et al.  Tight logic programs , 2003, Theory and Practice of Logic Programming.

[12]  Rina Dechter,et al.  Constraint Processing , 1995, Lecture Notes in Computer Science.

[13]  Vladimir Lifschitz,et al.  Logic Programming and Nonmonotonic Reasoning: 7th International Conference, Lpnmr 2004, Fort Lauderdale, Fl. Isa. Kamiaru 6-8. 2004: Proceedings (LECTURE NOTES IN COMPUTER SCIENCE) , 2004 .

[14]  Wolfgang Faber,et al.  Pruning Operators for Disjunctive Logic Programming Systems , 2006, Fundam. Informaticae.

[15]  Wolfgang Faber,et al.  A backjumping technique for Disjunctive Logic Programming , 2006, AI Commun..

[16]  Wolfgang Faber,et al.  Experimenting with Look-Back Heuristics for Hard ASP Programs , 2007, LPNMR.

[17]  M. Gelfond,et al.  Disjunctive Defaults , 1991 .

[18]  Wolfgang Faber,et al.  Enhancing Eciency and Expressiveness in Answer Set Programming Systems , 2002 .

[19]  M. Schaefer,et al.  Completeness in the Polynomial-Time Hierarchy A Compendium ∗ , 2008 .

[20]  Gerald Pfeifer,et al.  Enhancing disjunctive logic programming systems by SAT checkers , 2003, Artif. Intell..

[21]  Georg Gottlob,et al.  On the computational cost of disjunctive logic programming: Propositional case , 1995, Annals of Mathematics and Artificial Intelligence.

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

[23]  Martin Gebser,et al.  GrinGo : A New Grounder for Answer Set Programming , 2007, LPNMR.

[24]  Joohyung Lee,et al.  Loop Formulas for Disjunctive Logic Programs , 2003, ICLP.

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

[26]  Martin Gebser,et al.  Conflict-Driven Answer Set Solving , 2007, IJCAI.

[27]  Joohyung Lee,et al.  A Model-Theoretic Counterpart of Loop Formulas , 2005, IJCAI.

[28]  Yuliya Lierler,et al.  Elementary Sets of Logic Programs , 2006, AAAI.

[29]  J. P. Marques,et al.  GRASP : A Search Algorithm for Propositional Satisfiability , 1999 .

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

[31]  Jia-Huai You,et al.  Unfolding partiality and disjunctions in stable model semantics , 2000, TOCL.

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

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

[34]  Stefan Woltran,et al.  Simplifying Logic Programs Under Uniform and Strong Equivalence , 2004, LPNMR.

[35]  Chitta Baral,et al.  Knowledge Representation, Reasoning and Declarative Problem Solving , 2003 .

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

[37]  V. Rich.  Personal communication , 1989, Nature.

[38]  Toniann Pitassi,et al.  Propositional Proof Complexity: Past, Present and Future , 2001, Bull. EATCS.

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

[40]  Martin Gebser,et al.  Advanced Preprocessing for Answer Set Solving , 2008, ECAI.

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