基于命题逻辑概率赋值的近似推理模式

Approximate Reasoning Model Based on Probability Valuation of Propositional Logic

将命题逻辑的赋值域由二值{0,1}推广到给定的概率空间,引进命题公式的概率赋值,概率赋值是经典命题逻辑赋值及各种真度概念的推广.利用概率赋值引入命题公式的概率真度、不可靠度、基于独立事件赋值集的概率真度等概念,通过讨论概率真度的性质,表明概率真度在全体命题公式集F(S)上满足Kolmogorov公理.证明全部命题公式基于独立事件赋值集的真度之集在[0,1]中无孤立点,以及在命题逻辑形式推演中,一个有效推理结论的不可靠度不超过各前提的不可靠度与其必要度的乘积之和等结论.在概率赋值的基础上,引进命题公式集的a.e.结论、依概率结论、依概率真度结论等概念,讨论这些概念之间的联系,并提出两个不同类型的近似推理模式.

The value domain of proposition logic is extended from two values{0,1} to a probability space, and hence the concept of probability valuation of propositional formulas is introduced. Probability valuation is a generalization of classical propositional valuation and various truth degrees. Based on probability valuation, the concepts of probability truth degree, uncertainty degree, probability truth degree based on the set of all probability valuation of formulas on independent events are introduced. Grounded on the discussion of the properties of probability truth degree, probability truth degree satisfies Kolmogorov axioms on the entire set of propositional formulas. It is proved that the set of probability truth degrees of all formulas based on the set of all probability valuation on independent events has no isolated points in [0,1]. In the form of deduction in propositional logic, the uncertainty degree of conclusion is less than or equal to the sum of the product of uncertainty degree of each premise and its essentialness degree in a formal inference. Based on probability valuation, some concepts of a. e. conclusion, conclusion in probability and conclusion in probability truth of a formula set are introduced, and the relations between these concepts are discussed. Moreover, two different approximate reasoning models based on probability valuation are proposed.