The Implementation of a Product Fuzzy DPLL Solver

Ivor Uhliarik

Abstract

The area of automated theorem proving in fuzzy logics has been revisited during the last decade with novel approaches, mathematical foundations, and software. However, only a few of these are capable of dealing with logics based on the product t-norm. The existing methods are usually based on (1) translations into satisfiability modulo theories, (2) evolutionary algorithms, and (3) fuzzy extensions of classical-logic procedures, such as the Davis-Putnam-Logemann-Loveland (DPLL) procedure. In this paper we present the results of our work on the first DPLL-based solver for product propositional logic extended with the Monteiro-Baaz ∆ operator and order (≺,≖) operators. Our contribution consists of the refinement and completion of our previously proposed deterministic algorithm and the working implementation of the solver. Comparing to other approaches, the essential difference of ours lies in its self-containment—it is not based on translations into other systems, which provides possibilities for feasible modifications or further optimizations. The solver yields answers to the 1-satisfiability and validity problems, and is available for download and use as free and open-source software.

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