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- W4366999676 abstract "In cite{LC, LCMF}, it was introduced a logic (called Six ) associated to a class of algebraic structures known as {em involutive Stone algebras}. This class of algebras, denoted by Sto , was considered by the first time in cite{CS1} as a tool for the study of certain problems connected to the theory of finite--valued L ukasiewicz--Moisil algebras. In fact, Six is the logic that preserves degrees of truth with respect to the class Sto . Among other things, it was proved that Six is a 6--valued logic that is a {em Logic of Formal Inconsistency} (LFI ); moreover, it is possible to define a consistency operator in terms of the original set of connectives. A Gentzen-style system (which does not enjoy the cut--elimination property) for Six was given. Besides, in cite{LCMF}, it was shown that Six is matrix logic that is determined by a finite number of matrices; more precisely, four matrices. However, this result was further sharpened in cite{SMUR} proving that just one of these four matrices determine Six , that is, Six can be determined by a single 6--element logic matrix. In this work, taking advantage of this last result, we apply a method due to Avron, Ben-Naim and Konikowska cite{Avron02} to present different Gentzen systems for Six enjoying the cut--elimination property. This allows us to draw some conclusions about the method as well as to propose additional tools for the streamlining process. Finally, we present a decision procedure for Six based in one of these systems." @default.
- W4366999676 created "2023-04-27" @default.
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- W4366999676 date "2023-04-23" @default.
- W4366999676 modified "2023-09-30" @default.
- W4366999676 title "Cut-free sequent-style systems for a logic associated to involutive Stone algebras" @default.
- W4366999676 doi "https://doi.org/10.48550/arxiv.2304.11621" @default.
- W4366999676 hasPublicationYear "2023" @default.
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