Inferential Interpretations of Many-Valued Logics

Abstract

Non-Tarskian interpretations of many-valued logics have been widely explored in the logic literature. The development of non-tarskian conceptions of logical consequence set the theoretical foundations for rediscovering well-known (Tarskian) many-valued logics. One may find in distinct authors many novel interpretations of many-valued systems. They are produced through a type of procedure which consists in altering the semantic structure of Tarskian many-valued logics in order to output a non-Tarskian interpretation of these logics. Through this type of transformation the paper explores a uniform way of transforming finitely many-valued Tarskian logics into their non-Tarskian interpretation. Some general properties of carrying out this type of procedure are studied, namely the dualities between these logics and the conditions under which negation-explosive and negation-complete Tarskian logics become non-explosive.