2011•Dianzi xuebaoRequires access

The Properties of Truth Degrees of Formulas in (3n+1)-Valued Logic System R_0L

Qiong Zhang

Abstract

Based on the idea of quantitative logic,the definition of the truth degrees of formulas is proposed in(3n+1)-valued propositional logic system R0L,and its main properties are discussed.The integral representation of the truth degrees of formulas is given,the truth degree modus ponens and truth degree hypothetical syllogism are proved.The concepts of similarity degree and pseudo-metric among formulas are introduced by means of the truth degree.The work of this paper is the base for establishing the framework of approximate reasoning on(3n+1)-valued propositional logic system R0L.

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Key concepts: Truth function, Tautology (logic), Propositional calculus, Mathematics, Truth value, Modus ponens, Intuitionistic logic, Coherence theory of truth