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In \cite{LC, LCMF}, it was introduced a logic (called \Six ) associated to aclass of algebraic structures known as {\em involutive Stone algebras}. Thisclass 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 theoryof finite--valued \L ukasiewicz--Moisil algebras. In fact, \Six\ is the logicthat 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 definea consistency operator in terms of the original set of connectives. AGentzen-style system (which does not enjoy the cut--elimination property) for\Six\ was given. Besides, in \cite{LCMF}, it was shown that \Six\ is matrixlogic that is determined by a finite number of matrices; more precisely, fourmatrices. However, this result was further sharpened in \cite{SMUR} provingthat just one of these four matrices determine \Six , that is, \Six\ can bedetermined by a single 6--element logic matrix.  In this work, taking advantage of this last result, we apply a method due toAvron, Ben-Naim and Konikowska \cite{Avron02} to present different Gentzensystems for \Six\ enjoying the cut--elimination property. This allows us todraw some conclusions about the method as well as to propose additional toolsfor the streamlining process. Finally, we present a decision procedure for\Six\ based in one of these systems.

Cut-free sequent-style systems for a logic associated to involutive Stone algebras