Constraint tableaux for two-dimensional fuzzy logics
Abstract
We introduce two-dimensional logics based on ukasiewicz and G\"odel 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.
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