Abstract

We study generalized deduction rules of cut and weakening in the context of equational fragment of Pavelka-style fuzzy logic using complete residuated lattices as the structures of truth degrees. The deduction rules in question are parameterized by a truth stresser, an additional unary operation on the structure of truth degrees. It is shown that the deductive system of fuzzy Horn logic can be replaced by several equivalent systems which use cut and weakening instead of the monotony rule