  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.
