Approximate Reasoning Model Based on Probability Valuation of Propositional Logic
ZHANG Jia-Lu1, CHEN Xue-Gang2, WU Xia1
1.School of Mathematics and Finance, Xiangnan University, Chenzhou 423000 2.School of Software and Communication Engineering, Xiangnan University, Chenzhou 423000
Abstract 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.
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2015, Vol. 28 
