Constraint tableaux for two-dimensional fuzzy logics

Abstract

We introduce two-dimensional logics based on Lukasiewicz and Gödel logics to formalize paraconsitent fuzzy reasoning. The logics are interpreted on matrices, where the common underlying structure is the bi-lattice (twisted) product of the [0, 1] interval. The first (resp. second) coordinate encodes the positive (resp. negative) information one has about a statement. We propose constraint tableaux that provide a modular framework to address their completeness and complexity.