An SMT-Based solver for continuous t-norm based logics

Authors:
Amanda Vidal;Félix Bou;Lluís Godo
Affiliations:
Artificial Intelligence Research Institute (IIIA - CSIC), Bellaterra, Spain;Department of Probability, Logic and Statistics, Faculty of Mathematics, University of Barcelona (UB), Barcelona, Spain, Artificial Intelligence Research Institute (IIIA - CSIC), Bellaterra, Spain;Artificial Intelligence Research Institute (IIIA - CSIC), Bellaterra, Spain
Venue:
SUM'12 Proceedings of the 6th international conference on Scalable Uncertainty Management
Year:
2012

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Abstract

In the literature, little attention has been paid to the development of solvers for systems of mathematical fuzzy logic, even though there is an important number of studies on complexity and proof theory for them. In this paper, extending a recent approach by Ansótegui et al., we present ongoing work on an efficient and modular SMT-based solver for a wide family of continuous t-norm based fuzzy logics. The solver is able to deal with most famous fuzzy logics (including BL, Łukasiewicz, Gödel and Product); and for each of them, it is able to test, among others, satisfiability, tautologicity and logical consequence problems. Note that, unlike the classical case, these problems are not in general interdefinable in fuzzy logics. Some empirical results are reported at the end of the paper.