A Structural Approach to Reasoning with Quantified Boolean Formulas

In this paper we approach the problem of reasoning with quantified Boolean formulas (QBFs) by combining search and resolution, and by switching between them according to structural properties of QBFs. We provide empirical evidence that QBFs which cannot be solved by search or resolution alone, can be solved by combining them, and that our approach makes a proof-of-concept implementation competitive with current QBF solvers.

[1]  Anand S. Rao,et al.  An architecture for real-time reasoning and system control , 1992, IEEE Expert.

[2]  Luca Pulina,et al.  Treewidth: A Useful Marker of Empirical Hardness in Quantified Boolean Logic Encodings , 2008, LPAR.

[3]  Moshe Y. Vardi,et al.  Symbolic Decision Procedures for QBF , 2004, CP.

[4]  Hubie Chen,et al.  From Pebble Games to Tractability: An Ambidextrous Consistency Algorithm for Quantified Constraint Satisfaction , 2005, CSL.

[5]  Martha E. Pollack,et al.  Overloading Intentions for Efficient Practical Reasoning , 1991 .

[6]  Georg Gottlob,et al.  A Comparison of Structural CSP Decomposition Methods , 1999, IJCAI.

[7]  Edmund H. Durfee,et al.  Using Abstraction in Planning and Scheduling , 2014 .

[8]  M. Winikoff,et al.  Declarative & Procedural Goals in Intelligent Agent Systems , 2002, KR.

[9]  Michael Winikoff,et al.  Avoiding Resource Conflicts in Intelligent Agents , 2002, ECAI.

[10]  Marco Schaerf,et al.  An Algorithm to Evaluate Quantified Boolean Formulae , 1998, AAAI/IAAI.

[11]  Georg Gottlob,et al.  The Complexity of Quantified Constraint Satisfaction Problems under Structural Restrictions , 2005, IJCAI.

[12]  Ronen I. Brafman,et al.  Planning with Concurrent Interacting Actions , 1997, AAAI/IAAI.

[13]  Hans Kleine Büning,et al.  Resolution for Quantified Boolean Formulas , 1995, Inf. Comput..

[14]  Hans L. Bodlaender,et al.  A linear time algorithm for finding tree-decompositions of small treewidth , 1993, STOC.

[15]  Martha E. Pollack,et al.  Evaluating new options in the context of existing plans , 2001, Artif. Intell..

[16]  Michael Winikoff,et al.  Detecting & exploiting positive goal interaction in intelligent agents , 2003, AAMAS '03.

[17]  Edmund H. Durfee,et al.  Identifying and Resolving Conflicts among Agents with Hierarchical Plans , 1999 .

[18]  S. Malik,et al.  Validating the result of a quantified Boolean formula (QBF) solver: theory and practice , 2005, Proceedings of the ASP-DAC 2005. Asia and South Pacific Design Automation Conference, 2005..

[19]  Javier Larrosa,et al.  Boosting Search with Variable Elimination in Constraint Optimization and Constraint Satisfaction Problems , 2003, Constraints.

[20]  Rina Dechter,et al.  Resolution versus Search: Two Strategies for SAT , 2000, Journal of Automated Reasoning.

[21]  Armando Tacchella,et al.  Clause/Term Resolution and Learning in the Evaluation of Quantified Boolean Formulas , 2006, J. Artif. Intell. Res..

[22]  Fahiem Bacchus,et al.  Binary Clause Reasoning in QBF , 2006, SAT.

[23]  HarlandJames,et al.  Representation and reasoning for goals in BDI agents , 2002 .

[24]  Moshe Y. Vardi,et al.  Fixed-Parameter Hierarchies inside PSPACE , 2006, 21st Annual IEEE Symposium on Logic in Computer Science (LICS'06).

[25]  Armin Biere,et al.  Effective Preprocessing in SAT Through Variable and Clause Elimination , 2005, SAT.

[26]  Marcus J. Huber.  JAM: a BDI-theoretic mobile agent architecture , 1999, AGENTS '99.

[27]  Nils J. Nilsson,et al.  Artificial Intelligence , 1974, IFIP Congress.

[28]  Michael Wooldridge,et al.  A Formal Specification of dMARS , 1997, ATAL.

[29]  `# Clavicle —? etiology' , 1996 .

[30]  Edmund H. Durfee,et al.  Theory for Coordinating Concurrent Hierarchical Planning Agents Using Summary Information , 1999, AAAI/IAAI.

[31]  Marco Benedetti,et al.  sKizzo: A Suite to Evaluate and Certify QBFs , 2005, CADE.

[32]  Armin Biere,et al.  Resolve and Expand , 2004, SAT.