Constraint tableaux for two-dimensional fuzzy logics

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 $[0,1]$ 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.