A Simple Modal Encoding of Propositional Finite Many-Valued Logics

We present a method for testing the validity for any finite manyvalued logic by using simple transformations into the validity problem for von Wright’s logic of elsewhere. The method provides a new original viewpoint on finite many-valuedness. Indeed, we present a uniform modal encoding of any finite many-valued logic that views truth-values as nominals. Improvements of the transformations are discussed and the translation technique is extended to any finite annotated logic. Using similar ideas, we conclude the paper by defining transformations from the validity problem for any finite many-valued logic into TAUT (the validity problem for the classical propositional calculus). As already known, this sharply illustrates that reasoning within a finite many-valued logic can be naturally and easily encoded into a twovalued logic. All the many-one reductions in the paper are tight since they require only time in O(n.log n) and space in O(log n). Key-words: finite many-valued logic, modal logic of elsewhere, manyone reduction