Propositional fuzzy logics: Decidable for some (algebraic) operators; Undecidable for more complicated ones

If we view fuzzy logic as a logic, i.e., as a particular case of a multi-va lued logic, then one of the most natural questions to ask is whether the co rresponding propositional logic is decidable, i.e., does there exist an alg orithm that, given two propositional formulas F and G, decides whether thes e two formulas always have the same truth value. It is known that the simpl est fuzzy logic, in which & = min and v = max, is decidable. In this paper, we prove a more general result: that all propositional fuzzy logics with a lgebraic operations are decidable. We also show that this result cannot be generalized further, e.g., no deciding algorithm is possible for logics in which operations are algebraic with constructive (nonalgebraic) coefficient s. (C) 1999 John Wiley & Sons, Inc.