Propositional fuzzy logics based on Frankt - norms : A comparisonErich

Among various approaches to fuzzy logics, we have chosen two of them, which are built up in a similar way. Although starting from diierent basic logical connectives, they both use interpretations based on Frank t-norms. Diierent interpretations of the implication lead to diierent axiomatizations, but most logics studied here are complete. We compare the properties, advantages and disadvantages of the two approaches. We deal also with logics containing innnitary conjunctions , and we show that they are semantically \stronger" than all the other logics studied in this paper. 1 Frank t-norms Triangular norms were introduced in the framework of probabilistic metric spaces 33, 32, 34], based on ideas rst presented in 22], and they are applied in several elds, e.g., in fuzzy sets 35], fuzzy logics 2, 14, 28] and their applications , but also in the theory of generalized measures 1, 19] and nonlinear diierential and diierence equations 27]. A triangular norm (t-norm for short) is a commutative, associative, non-decreasing operation T : 0; 1] 2 ! 0; 1] with neutral element 1. An immediate consequence of the commutativity, the monotonicity and the boundary