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In this paper we consider the class of truth-functional many-valued logicswith a finite set of truth-values. The main result of this paper is thedevelopment of a new \emph{binary} sequent calculi (each sequent is a pair offormulae) for many valued logic with a finite set of truth values, and ofKripke-like semantics for it that is both sound and complete. We did not usethe logic entailment based on matrix with a strict subset of designated truthvalues, but a different new kind of semantics based on the generalization ofthe classic 2-valued truth-invariance entailment. In order to define thisnon-matrix based sequent calculi, we transform many-valued logic into positive2-valued multi-modal logic with classic conjunction, disjunction and finite setof modal connectives. In this algebraic framework we define an uniquelydetermined axiom system, by extending the classic 2-valued distributive latticelogic (DLL) by a new set of sequent axioms for many-valued logic connectives.Dually, in an autoreferential Kripke-style framework we obtain a uniquelydetermined frame, where each possible world is an equivalence class ofLindenbaum algebra for a many-valued logic as well, represented by a truthvalue.

Binary Sequent Calculi for Truth-invariance Entailment of Finite Many-valued Logics