Embedding Godel propositional logic into Prior's tense logic
Stefano Aguzzoli, Brunella Gerla, Vincenzo Marra · 2008
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 infinite-valued propositional logic into a schematic extension of Prior’s bi-modal 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 superintu-itionistic logics. For the reader’s convenience we include a short dis-cussion of the latter results.