Abstract The probabilistic truth degree functions of propositions in n-valued ukasiewicz propositional logic are abstracted as a modality,and their three basic identities are abstracted as axioms of the modality. Then,a modal logic system for reasoning about probabilistic truth degrees of propositions is proposed. The syntax and semantics are constructed. The completeness theorem with respect to probabilistic truth degree functions is finally obtained. A logic foundation is set for probabilistically quantitative logic.
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2013, Vol. 26 
