The aim of this paper is to provide a methodology for turning a known crisp logic into a fuzzy system. We require of the methodology that it be meaningful in general terms, using processes which are independent of the notion of fuzziness, and that it yield a considerable number of known fuzzy systems.
Fuzzy logics based on t-norms and their residua have been investigated extensively from a semantic perspective but a unifying proof theory for these logics has, until recently, been lacking. In this paper we survey results of the authors and others which show that a suitable proof-theoretic framework for fuzzy logics is provided by hypersequents, a natural generalization of Gentzen-style sequents. In particular we present hypersequent calculi for the logic of left-continuous t-norms MTL and related...