Tableau Calculus for Basic Fuzzy Logic BL

Abstract

In this paper we present a tableau calculus for BL, basic fuzzy logic introduced by Petr Hájek in his monograph Metamathematics of Fuzzy Logic. We show that it is sound and complete with respect to continuous t-norms, and demonstrate the refutational procedure and the search for models procedure on a selected example. The idea of the calculus is based on the decomposition theorem for a continuous t-norm, by which this operation is shown to be equivalent to the ordinal sum of a family of t-norms defined on countably many intervals. © Springer International Publishing Switzerland 2014.