The complexity of facets resolved
Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
Propositional circumscription and extended closed-world reasoning are &Pgr;p2-complete
Theoretical Computer Science
A Distributed Algorithm to Evaluate Quantified Boolean Formulae
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
On Indefinite Databases and the Closed World Assumption
Proceedings of the 6th Conference on Automated Deduction
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COCO '00 Proceedings of the 15th Annual IEEE Conference on Computational Complexity
Algorithms for Computing Minimal Unsatisfiable Subsets of Constraints
Journal of Automated Reasoning
Relaxations for Compiled Over-Constrained Problems
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
The equivalence problem for regular expressions with squaring requires exponential space
SWAT '72 Proceedings of the 13th Annual Symposium on Switching and Automata Theory (swat 1972)
On Approaches to Explaining Infeasibility of Sets of Boolean Clauses
ICTAI '08 Proceedings of the 2008 20th IEEE International Conference on Tools with Artificial Intelligence - Volume 01
Does This Set of Clauses Overlap with at Least One MUS?
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Redundancy in logic I: CNF propositional formulae
Artificial Intelligence
The complexity of closed world reasoning and circumscription
AAAI'90 Proceedings of the eighth National conference on Artificial intelligence - Volume 1
Counterexample guided abstraction refinement algorithm for propositional circumscription
JELIA'10 Proceedings of the 12th European conference on Logics in artificial intelligence
cmMUS: a tool for circumscription-based MUS membership testing
LPNMR'11 Proceedings of the 11th international conference on Logic programming and nonmonotonic reasoning
Proceedings of the 14th international conference on Theory and application of satisfiability testing
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
On improving MUS extraction algorithms
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
Abstraction-based algorithm for 2QBF
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
Advanced conflict-driven disjunctive answer set solving
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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This paper tackles the problem of deciding whether a given clause belongs to some minimally unsatisfiable subset (MUS) of a formula, where the formula is in conjunctive normal form (CNF) and unsatisfiable. Deciding MUS-membership helps the understanding of why a formula is unsatisfiable. If a clause does not belong to any MUS, then removing it will certainly not contribute to restoring the formula's consistency. Unsatisfiable formulas and consistency restoration in particular have a number of practical applications in areas such as software verification or product configuration. The MUS-membership problem is known to be in the second level of polynomial hierarchy, more precisely it is Σ2P -complete. Hence, quantified Boolean formulas (QBFs) represent a possible avenue for tackling the problem. This paper develops a number of novel QBF formulations of the MUS-membership problem and evaluates their practicality using modern off-the-shelf solvers.