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Generalization of the fundamental theorem of probability logic in multi-valued propositional logic. (Chinese) Zbl 1249.03012
Summary: By means of probability measure space, the concept of probability satisfying the Kolmogorov axioms is introduced into the n-valued Łukasiewicz logical system. The fundamental theorem of probability logic is proved and generalized in the n-valued Łukasiewicz logical system, so the estimation of uncertainty of conclusions in inference is improved. The basic methods of probability logic are introduced into quantitative logic and a more general logic metric space is obtained. The MP and HS rules of probability are proved by the fundamental theorem of probability logic, giving the generalization of the MP and HS rules of truth.
MSC:
03B48Probability logic; inductive logic
03B50Many-valued logic