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TRANSLATING FROM ŁUKASIEWICZ’S LOGICS INTO CLASSICAL LOGIC: IS IT POSSIBLE?

Ítala M. Loffredo D’Ottaviano, Hércules Araújo Feitosa

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Abstract

This work presents some basic results on a theory of translations between logics and a short revision about Łukasiewicz’s logics. Then, it is shown, using facts about algebraic semantics, that there is a conservative translation from every finite Łukasiewicz’s logic into classical logic. However, this is not a constructive result.

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What this paper is about

This work presents some basic results on a theory of translations between logics and a short revision about Łukasiewicz’s logics. Then, it is shown, using facts about algebraic semantics, that there is a conservative translation from every finite Łukasiewicz’s logic into classical logic. However, this is not a constructive result.

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OpenAlex reports 2 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This work presents some basic results on a theory of translations between logics and a short revision about Łukasiewicz’s logics. Then, it is shown, using facts about algebraic semantics, that there is a conservative translation from every finite Łukasiewicz’s logic into classical logic. However, this is not a constructive result.

Key concepts: Łukasiewicz logic, Monoidal t-norm logic, Algebraic semantics, Constructive, Intuitionistic logic, Algebra over a field, Classical logic, T-norm fuzzy logics

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