Bucket elimination: a unifying framework for reasoning
Artificial Intelligence
The SAT problem of signed CNF formulas
Labelled deduction
Solving weighted CSP by maintaining arc consistency
Artificial Intelligence
New inference rules for efficient Max-SAT solving
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Existential arc consistency: getting closer to full arc consistency in weighted CSPs
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Resolution in Max-SAT and its relation to local consistency in weighted CSPs
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
A complete calculus for Max-SAT
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
New inference rules for Max-SAT
Journal of Artificial Intelligence Research
Resolution procedures for multiple-valued optimization
Information Sciences: an International Journal
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Recently defined resolution calculi for Max-SAT and signed Max-SAT have provided a logical characterization of the solving techniques applied by Max-SAT and WCSP solvers. In this paper we first define a new resolution rule, called signed Max-SAT parallel resolution, and prove that it is sound and complete for signed Max-SAT. Second, we define a restriction and a generalization of the previous rule called, respectively, signed Max-SAT i-consistency resolution and signed Max-SAT (i,j)-consistency resolution. These rules have the following property: if a WCSP signed encoding is closed under signed Max-SAT i-consistency, then the WCSP is i-consistent, and if it is closed under signed Max-SAT (i,j)-consistency, then the WCSP is (i,j)-consistent. A new and practical insight derived from the definition of these new rules is that algorithms for enforcing high order consistency should incorporate an efficient and effective component for detecting minimal unsatisfiable cores. Finally, we describe an algorithm that applies directional soft consistency with the previous rules.