Fuzzy refutations for probability and multivalued logics

AbstractThe deductive apparatus of a fuzzy logic is usually proposed in Hilbert's style by fixing a fuzzy subset of logical axioms and a set of fuzzy inference rules. We sketch a “refutation approach” to fuzzy deduction. In particular, this enables us to face probability logic as a particular fuzzy refutation system in the framework of fuzzy logic. Namely, we propose a refutation system in which the probabilistic theories correspond to the lower envelopes and the complete probabilistic theories correspond to the probabilities. Finally, we apply the concept of fuzzy refutation system to multivalued logic