Translating non-classical logics into the classical logic by using hidden variables

  • Juan C. Agudelo-Agudelo


It is here proposed a method for constructing conservative translations of logics characterized by ‘dyadic semantics’ (a kind of non-truth-functional bivalued semantics) into the classical logic. The method particularly works for several finite many-valued logics and paraconsistent logics. The translation method uses ‘hidden variables’, which are propositional variables used to represent the indeterminism that arises when non-classical logics are provided of bivalued semantics. Then, it is shown that intuitionistic logic, for instance, is not characterizable by dyadic semantics, then the translation method here proposed do not applied for this logic. Moreover, it is provided an alternative method (not based on dyadic semantics) for constructing conservative translations of any finite many-valued logic into the classical logic. In this translation method ‘hidden variables’ are also used, but in this case to represent the degree of true or falsehood of propositions.