Axiomatizations of t-norm based logics – A survey

Abstract

 In fuzzy logic in wider sense, i.e. in the field of fuzzy sets applications, t-norms got a prominent rôle in recent times. In many-valued logic, the ŁUKASIEWICZ systems, the GÖDEL sytems, and also the product logic all are t-norm based systems. The present paper discusses the more general problem of the adequate axiomatizability for such t-norm based logical systems in general, surveying results of the last years. The main emphasis in the present paper is on propositional logic.