Resolution-based theorem proving for many-valued logics
Journal of Symbolic Computation
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
Bucket elimination: a unifying framework for reasoning
Artificial Intelligence
The SAT problem of signed CNF formulas
Labelled deduction
A Framework for Automated Reasoning in Multiple-Valued Logics
Journal of Automated Reasoning
Mini-buckets: A general scheme for bounded inference
Journal of the ACM (JACM)
Chaining Techniques for Automated Theorem Proving in Many-Valued Logics
ISMVL '00 Proceedings of the 30th IEEE International Symposium on Multiple-Valued Logic
CAMA: A Multi-Valued Satisfiability Solver
Proceedings of the 2003 IEEE/ACM international conference on Computer-aided design
Solving weighted CSP by maintaining arc consistency
Artificial Intelligence
Artificial Intelligence
Regular-SAT: A many-valued approach to solving combinatorial problems
Discrete Applied Mathematics
Exploiting multivalued knowledge in variable selection heuristics for SAT solvers
Annals of Mathematics and Artificial Intelligence
A logical approach to efficient Max-SAT solving
Artificial Intelligence
Inference rules for high-order consistency in weighted CSP
AAAI'07 Proceedings of the 22nd national conference on Artificial intelligence - Volume 1
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
In the quest of the best form of local consistency for weighted CSP
IJCAI'03 Proceedings of the 18th international joint conference on Artificial 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
A complete multi-valued SAT solver
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
A complete calculus for Max-SAT
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
Read-once resolution for unsatisfiability-based Max-SAT algorithms
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Hi-index | 0.07 |
Signed clausal forms offer a suitable logical framework for automated reasoning in multiple-valued logics. It turns out that the satisfiability problem of any finitely-valued propositional logic, as well as of certain infinitely-valued logics, can be easily reduced, in polynomial time, to the satisfiability problem of signed clausal forms. On the other hand, signed clausal forms are a powerful knowledge representation language for constraint programming, and have shown to be a practical and competitive approach to solving combinatorial decision problems. Motivated by the existing theoretical and practical results for the satisfiability problem of signed clausal forms, as well as by the recent logical and algorithmic results on the Boolean maximum satisfiability problem, in this paper we investigate the maximum satisfiability problem of propositional signed clausal forms from the logical and practical points of view. From the logical perspective, our aim is to define complete inference systems taking as a starting point the resolution-style calculi defined for the Boolean CNF case. The result is the definition of two sound and complete resolution-style rules, called signed binary resolution and signed parallel resolution for maximum satisfiability. From the practical perspective, our main motivation is to use the language of signed clausal forms along with the newly defined inference systems as a generic approach to solve combinatorial optimization problems, and not just for solving decision problems as so far. The result is the establishment of a link between signed logic and constraint programming that provides a concise and elegant logical framework for weighted constraint programming.