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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 $v\left(A\right)⩾\zeta$ (or $v\left(A\right)>\zeta$, where $\zeta \in \left[0,1\right]$) in the set of all valuations is considered. The concepts of $\zeta$-truth degree and ${\zeta }^{+}$-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 $\sigma$-($\zeta$-tautology) and $\sigma$-(${\zeta }^{+}$-tautology) are defined. Moreover, relationships between $\zeta$-truth degrees (${\zeta }^{+}$-truth degrees) and generalized tautologies together with the graded generalized tautologies are discussed and the general reference rules endowed with $\zeta$-truth degrees are proved.
##### MSC:
 03B50 Many-valued logic 03B48 Probability logic; inductive logic 03B52 Fuzzy logic; logic of vagueness