MNiBLoS: A SMT-based solver for continuous t-norm based logics and some of their modal expansions

In the literature, little attention has been paid to the development of solvers for systems of mathematical fuzzy logic, and in particular, there are few works concerned with infinitely-valued logics. In this paper it is presented mNiBLoS (a modal Nice BL-Logics Solver): a modular SMT-based solver complete with respect to a wide family of continuous t-norm based fuzzy modal logics (both with finite and infinite universes), restricting the modal structures to the finite ones. At the propositional level, the solver works with some of the best known infinitely-valued fuzzy logics (including BL, Łukasiewicz, Gödel and product logics), and with all the continuous t-norm based logics that can be finitely expressed in terms of the previous ones; concerning the modal expansion, mNiBLoS imposes no boundary on the cardinality of the modal structures considered. The solver allows to test 1-satisfiability of equations, tautologicity and logical consequence problems. The logical language supported extends the usual one of fuzzy modal logics with rational constants and the Monteiro-Baaz Δ operator. The code of mNiBLoS is of free distribution and can be found in the web page of the author. © 2016 Elsevier Inc.This work was supported by the CSIC Intramural project 201450E045:“Logal: Lógica y algoritmos”, the joint project of Austrian Science Fund (FWF) I1897-N25 and Czech Science Foundation (GACR) 15-34650L, the institutional support RVO:67985807 and the MINECO project EdeTRI:TIN2012-39348-C02-01. The author wishes to thank the anonymous reviewers for their useful commentaries.Peer Reviewe