Constraint tableaux for two-dimensional fuzzy logics

Marta Bílková; Sabine Frittella; Daniil Kozhemiachenko

doi:10.1007/978-3-030-86059-2_2

paper

Constraint tableaux for two-dimensional fuzzy logics

arXiv:2105.07217 · doi:10.1007/978-3-030-86059-2_2

Abstract

We introduce two-dimensional logics based on Łukasiewicz and Gödel logics to formalize paraconsistent 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.