Abstract

ABSTRACT. This paper discusses the general problem of translation functions between logics, given in axiomatic form, and in particular, the problem of determining when two such logics are “synonymous ” or “translationally equivalent. ” We discuss a proposed formal definition of translational equivalence, show why it is reasonable, and also discuss its relation to earlier definitions in the literature. We also give a simple criterion for showing that two modal logics are not translationally equivalent, and apply this to well-known examples. Some philosophical morals are drawn concerning the possibility of having two logical systems that are “empirically distinct ” but are both translationally equivalent to a common logic. KEY WORDS: modal logic, synonymy, translation 1.

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