Satisfiability in many-valued sentential logic is NP-complete
Theoretical Computer Science
Resolution-based theorem proving for many-valued logics
Journal of Symbolic Computation
Ordered chaining calculi for first-order theories of transitive relations
Journal of the ACM (JACM)
A Linear Format for Resolution With Merging and a New Technique for Establishing Completeness
Journal of the ACM (JACM)
The SAT problem of signed CNF formulas
Labelled deduction
A Framework for Automated Reasoning in Multiple-Valued Logics
Journal of Automated Reasoning
Finiteness in Infinite-Valued Σukasiewicz Logic
Journal of Logic, Language and Information
Automated deduction for many-valued logics
Handbook of automated reasoning
Transformations between Signed and Classical Clause Logic
ISMVL '99 Proceedings of the Twenty Ninth IEEE International Symposium on Multiple-Valued Logic
Chaining Techniques for Automated Theorem Proving in Many-Valued Logics
ISMVL '00 Proceedings of the 30th IEEE International Symposium on Multiple-Valued Logic
Journal of Symbolic Computation
Mapping Many-Valued CNF Formulas to Boolean CNF Formulas
ISMVL '05 Proceedings of the 35th International Symposium on Multiple-Valued Logic
Discrete Applied Mathematics
Automated theorem proving by resolution in non-classical logics
Annals of Mathematics and Artificial Intelligence
Binary resolution over complete residuated Stone lattices
Fuzzy Sets and Systems
Generalizing Boolean satisfiability II: theory
Journal of Artificial Intelligence Research
Solving non-Boolean satisfiability problems with stochastic local search
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Adapting Classical Inference Techniques To Multiple-Valued Logics Using Signed Formulas
Fundamenta Informaticae
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Signed binary resolution and hyperresolution belong to the basic resolution proof methods. Both the resolution methods are refutation sound and, under some finitary restrictions, refutation complete. Our aim is to investigate their refutational completeness in a more general case. We shall assume that clausal theories may be countable sets and the set of truth values an arbitrary one. There are unsatisfiable countable clausal theories for which there do not exist refutations by signed binary resolution and hyperresolution. We propose a criterion on the existence of a refutation of an unsatisfiable countable clausal theory by the investigated resolution methods. Two important applications of the achieved results to automated deduction in signed logic: Herbrand's theorem and a signed Davis-Putnam-Logemann-Loveland (DPLL) procedure will be discussed.