Constraint tableaux for two-dimensional fuzzy logics
Marta B\'ilkov\'a, Sabine Frittella, Daniil Kozhemiachenko
TL;DR
This paper introduces two-dimensional fuzzy logics based on lasiewicz and Gf6del logics, using bi-lattice matrices to formalize paraconsistent fuzzy reasoning with a modular tableau framework.
Contribution
It presents a novel two-dimensional logic framework with constraint tableaux for completeness and complexity analysis in paraconsistent fuzzy reasoning.
Findings
Framework successfully formalizes paraconsistent fuzzy reasoning.
Constraint tableaux ensure modularity and facilitate completeness proofs.
Applicable to bi-lattice based fuzzy logic systems.
Abstract
We introduce two-dimensional logics based on \L{}ukasiewicz and G\"{o}del 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 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.
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