■ukasiewicz命题逻辑中命题的Borel概率真度理论和极限定理

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

通过视赋值集为通常乘积拓扑空间,利用其上的Borel概率测度在n值及连续值■ukasiewicz命题逻辑系统中引入了命题的Borel概率真度概念,讨论了它的基本性质,特别是给出了n值情形中概率真度函数的积分表示定理,并得到了其与连续情形概率真度函数之间关系的一个极限定理.结果表明,计量逻辑学中命题的真度概念只是所研究工作的一个特例,因而基于概率真度概念可以为不确定性推理建立一种更为宽泛的计量化模型.

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 [0,1 ]-valued Lukasiewicz 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.