Theory of Borel Probability Truth Degrees of Propositions in ■ukasiewicz Propositional Logics and a Limit Theorem

By means of Borel probability measures on the valuation set endowed with the usual product topology,the notion of probability truth degrees of propositions in n-valued and -valued ■ukasiewicz propositional logics is introduced.Its basic properties are investigated,and the integral representation theorem and the limit theorem of probability truth degree functions in n-valued case,in particular,are obtained.Theses results show that the notion of truth degree existing in quantitative logic is just a particular case of Borel probability truth degrees,and a more general quantitative model based on the notion of Borel probability truth degree for uncertainty reasoning can be then established.