Title: Proof Systems for Gödel Logics with an Involution
Abstract: G~, the extension of Gödel logic G with an invo-lutive negation, has many applications, like its use as a fuzzy paraconsistent logic. In this paper we provide analytic proof systems for both the truth-preserving and the degree-preserving versions of G~, as well as to its proper extensions in its language. In addition, we provide particularly simple Hilbert-type axiomatizations of these logics, which (unlike previous such axiomatizations) do not use Baaz' Δ operator. Instead, we follow a suggestion made (and left open) in [16], and base our systems on using, in addition to (MP), the rule (CP). (from φ → ψ infer ¬ψ → ¬φ). This establishes an interesting connection between G~, and some major modal logics (like B and S 5).
Publication Year: 2021
Publication Date: 2021-05-01
Language: en
Type: article
Indexed In: ['crossref']
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