Fuzzy Horn Logic

Abstract

Implications between identities have been widely studied in universal algebra. There are numerous results on implicationally defined classes of algebras and provability of implications from theories in form of implications. A survey on implications in the context of universal algebra can be found in monograph [97]. In this chapter, we suggest a generalization of the concept of an implication between identities in fuzzy setting and show that the results on (classical) Horn logic have their analogies in fuzzy setting. As in Chap. 3, we develop our logical calculus in Pavelka style.