 The algebraic semantics can be used for first-order fuzzy logics in a rather straightforward way: just change the definition of a \(\ast\)-structure of the previous section to a structure that, instead of the interval [0,1] and \(\ast\) and its residuum, uses an arbitary MTL-chain and its operation to compute truth-values of formulas. Given a propositional fuzzy logic, one can use this generalized semantics to obtain a recursively enumerable set of tautologies and a strong completeness theorem for a corresponding first-order Hilbert-style proof system.