The well-known Goedel translation embeds intuitionistic propositional logic into the modal logic S4. In this note, we use essentially the same translation to embed Goedel 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.
Embedding Gödel propositional logic into Prior's tense logic / S. Aguzzoli, B. Gerla, V. Marra - In: Proceedings of The 12th Conference on Information Processing and Management of Uncertainty in Knowledge-based Systems / [a cura di] L. Magdalena, M. Ojeda-Aciego, J.L. Verdegay. - Torremolinos (Malaga) : null, 2008. - pp. 992-999 (( Intervento presentato al 12. convegno IPMU 2008 tenutosi a Malaga nel 2008.
Embedding Gödel propositional logic into Prior's tense logic
S. AguzzoliPrimo
;V. MarraUltimo
2008
Abstract
The well-known Goedel translation embeds intuitionistic propositional logic into the modal logic S4. In this note, we use essentially the same translation to embed Goedel 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.Pubblicazioni consigliate
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