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- W2912590499 abstract "Abstract Involutive Stone algebras (or S-algebras) were introduced by R. Cignoli and M. Sagastume in connection to the theory of $n$-valued Łukasiewicz–Moisil algebras. In this work we focus on the logic that preserves degrees of truth associated to S-algebras named Six. This follows a very general pattern that can be considered for any class of truth structure endowed with an ordering relation, and which intends to exploit many-valuedness focusing on the notion of inference that results from preserving lower bounds of truth values, and hence not only preserving the value $1$. Among other things, we prove that Six is a many-valued logic (with six truth values) that can be determined by a finite number of matrices (four matrices). Besides, we show that Six is a paraconsistent logic. Moreover, we prove that it is a genuine Logic of Formal Inconsistency with a consistency operator that can be defined in terms of the original set of connectives. Finally, we study the proof theory of Six providing a Gentzen calculus for it, which is sound and complete with respect to the logic." @default.
- W2912590499 created "2019-02-21" @default.
- W2912590499 creator A5027425027 @default.
- W2912590499 creator A5073826642 @default.
- W2912590499 date "2018-11-29" @default.
- W2912590499 modified "2023-09-26" @default.
- W2912590499 title "On the logic that preserves degrees of truth associated to involutive Stone algebras" @default.
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- W2912590499 doi "https://doi.org/10.1093/jigpal/jzy071" @default.
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