Translating Non-classical Logics into Classical Logic by Using Hidden Variables

Abstract

Dyadic semantics is a sort of non-truth-functional bivalued semantics introduced in Caleiro et al. (in: Beziau J-Y (ed) Logica Universalis, Birkhauser, Basel, pp 169–189, 2005). Here we introduce an algorithmic procedure for constructing conservative translations of logics characterised by dyadic semantics into classical propositional logic. The procedure uses fresh propositional variables, which we call hidden variables, to represent the indeterminism of dyadic semantics. An alternative algorithmic procedure (not based on dyadic semantics) for constructing conservative translations of any finite-valued logic into classical logic is also introduced. In this alternative procedure hidden variables are also used, but in this case to represent the degree of true or falsehood of propositions.