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Theory of truth degrees of propositions in the logic system L n * . (English) Zbl 1104.03014
Summary: By means of the infinite product of uniformly distributed probability spaces of cardinality n the concept of truth degrees of propositions in the n-valued generalized Łukasiewicz propositional logic system L n * is introduced. It is proved that the set consisting of the truth degrees of all formulas is dense in [0, 1], and a general expression of truth degrees of formulas as well as a deduction rule of truth degrees is then obtained. Moreover, similarity degrees among formulas are proposed and a pseudo-metric is defined therefrom on the set of formulas, and hence a possible framework suitable for developing approximate reasoning theory in n-valued generalized Łukasiewicz propositional logic is established.
MSC:
03B50Many-valued logic
03B52Fuzzy logic; logic of vagueness
68T37Reasoning under uncertainty
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