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Quantitative research of generalized tautologies in n-valued propositional logic L n * . (Chinese) Zbl 1212.03011
Summary: By means of the infinite product of evenly distributed probability spaces, the proportion of the class of valuations which satisfies v(A)ζ (or v(A)>ζ, where ζ[0,1]) in the set of all valuations is considered. The concepts of ζ-truth degree and ζ + -truth degree in the n-valued R 0 -propositional logic system L n * are introduced in order to double-grade the concept of tautology. Also, the theories of σ-(ζ-tautology) and σ-(ζ + -tautology) are defined. Moreover, relationships between ζ-truth degrees (ζ + -truth degrees) and generalized tautologies together with the graded generalized tautologies are discussed and the general reference rules endowed with ζ-truth degrees are proved.
MSC:
03B50Many-valued logic
03B48Probability logic; inductive logic
03B52Fuzzy logic; logic of vagueness