Embedding Gödel propositional logic into Prior’s tense logic

Stefano Aguzzoli, Brunella Gerla, Vincenzo Marra.

The well-known Gödel translation embeds intuitionistic propositional logic into the modal logic S4. In this note, we use essentially the same translation to embed Gödel infinitevalued propositional logic into a schematic extension of Prior?s bimodal tense logic that allows finite chains only as flows of time. While our proofs use elementary techniques in many-valued algebraic logic, our embedding is strongly related to well-known results from the theory of modal companions to superintuitionistic logics. For the reader?s convenience we include a short discussion of the latter results.

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