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CORR
2011
Springer

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

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Binary Sequent Calculi for Truth-invariance Entailment of Finite Many-valued Logics
In this paper we consider the class of truth-functional many-valued logics with a finite set of truth-values. The main result of this paper is the development of a new binary sequent calculi (each sequent is a pair of formulae) for many valued logic with a finite set of truth values, and of Kripke-like semantics for it that is both sound and complete. We did not use the logic entailment based on matrix with a strict subset of designated truth values, but a different new kind of semantics based on the generalization of the classic 2-valued truthinvariance entailment. In order to define this non-matrix based sequent calculi, we transform many-valued logic into positive 2-valued multi-modal logic with classic conjunction, disjunction and finite set of modal connectives. In this algebraic framework we define an uniquely determined axiom system, by extending the classic 2-valued distributive lattice logic (DLL) by a new set of sequent axioms for many-valued logic connectives. Dually, i...
Zoran Majkic
Added 19 Aug 2011
Updated 19 Aug 2011
Type Journal
Year 2011
Where CORR
Authors Zoran Majkic
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