A modular reduction of regular logic to classical logic

Béjar, Ramón; Hähnle, Reiner; Manyà, Felip

doi:10.1109/ismvl.2001.924576

Cited by 20 publications

(19 citation statements)

References 16 publications

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“…A large body of research exists on encoding constraints into CNF [16,23,22,11,13,12,6,1,10,4]. In addition, dedicated encodings have been proposed for specific types of constraints, including cardinality constraints [2,3].…”

Section: Related Workmentioning

confidence: 99%

Towards Robust CNF Encodings of Cardinality Constraints

Marques-Silva

Lynce

Principles and Practice of Constraint Programming – CP 2007

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Abstract. Motivated by the performance improvements made to SAT solvers in recent years, a number of different encodings of constraints into SAT have been proposed. Concrete examples are the different SAT encodings for ≤ 1 (x1, . . . , xn) constraints. The most widely used encoding is known as the pairwise encoding, which is quadratic in the number of variables in the constraint. Alternative encodings are in general linear, and require using additional auxiliary variables. In most settings, the pairwise encoding performs acceptably well, but can require unacceptably large Boolean formulas. In contrast, linear encodings yield much smaller Boolean formulas, but in practice SAT solvers often perform unpredictably. This lack of predictability is mostly due to the large number of auxiliary variables that need to be added to the resulting Boolean formula. This paper studies one specific encoding for ≤ 1 (x1, . . . , xn) constraints, and shows how a state-of-the-art SAT solver can be adapted to overcome the problem of adding additional auxiliary variables. Moreover, the paper shows that a SAT solver may essentially ignore the existence of auxiliary variables. Experimental results indicate that the modified SAT solver becomes significantly more robust on SAT encodings involving ≤ 1 (x1, . . . , xn) constraints.

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Section: Related Workmentioning

confidence: 99%

Towards Robust CNF Encodings of Cardinality Constraints

Marques-Silva

Lynce

Principles and Practice of Constraint Programming – CP 2007

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“…The study of k-MVSAT(S) was started in [17] and further continued in [1,[5][6][7]10]. Manyà [17] established that 2-MVSAT is NP-complete using a reduction from the 3-coloring problem.…”

Section: Related Workmentioning

confidence: 99%

Deciding the Satisfiability of Propositional Formulas in Finitely-Valued Signed Logics

Chepoi

Creignou

Hermann

et al. 2008

38th International Symposium on Multiple Valued Logic (Ismvl 2008)

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Signed logic is a way of expressing the semantics of many-valued connectives and quantifiers in a formalism that is well-suited for automated reasoning. In this paper we consider propositional, finitely-valued formulas in clausal normal form. We show that checking the satisfiability of formulas with three or more literals per clause is either NP-complete or trivial, depending on whether the intersection of all signs is empty or not. The satisfiability of bijunctive formulas, i.e., formulas with at most two literals per clause, is decidable in linear time if the signs form a Helly family, and is NP-complete otherwise. We present a polynomial-time algorithm for deciding whether a given set of signs satisfies the Helly property. Our results unify and extend previous results obtained for particular sets of signs.

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“…Reductions of validity testing in many-valued logics to SAT checking in propositional logicsincluding a study of various possible optimizations, and various complexity studied -were studied in various papers, among which we mention e.g. [12][13][14]43]. In what follows we will refer to automated theorem proving in first order finitelyvalued logics.…”

Section: Resolution In Finitely-valued Logicsmentioning

confidence: 99%

Automated theorem proving by resolution in non-classical logics

Sofronie-Stokkermans

2007

Ann Math Artif Intell

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This paper is an overview of a variety of results, all centered around a common theme, namely embedding of non-classical logics into first order logic and resolution theorem proving. We present several classes of non-classical logics, many of which are of great practical relevance in knowledge representation, which can be translated into tractable and relatively simple fragments of classical logic. In this context, we show that refinements of resolution can often be used successfully for automated theorem proving, and in many interesting cases yield optimal decision procedures

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A modular reduction of regular logic to classical logic

Cited by 20 publications

References 16 publications

Towards Robust CNF Encodings of Cardinality Constraints

Towards Robust CNF Encodings of Cardinality Constraints

Deciding the Satisfiability of Propositional Formulas in Finitely-Valued Signed Logics

Automated theorem proving by resolution in non-classical logics

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