基于条件事件代数的贝叶斯网的逻辑推理

条件事件代数理论在数据融合系统中有着重要的应用前景,该理论可用来解决不确定性、概率性和模糊性推理问题。条件事件代数是在确保规则与条件概率相容的前提下,把布尔代数上的逻辑运算推广到条件事件(规则)集合中的逻辑代数系统。对于一些特殊的贝叶斯网(如多树型网络)已经有了一些可行的概率推理的算法,但到目前为止,还没有可行的逻辑推理的算法。随着对不确定性知识研究的深入,迫切需要具有逻辑推理的算法。论文介绍了乘积空间条件事件代数的定义和基本性质,提出了基于乘积空间条件事件代数的贝叶斯网的逻辑推理的算法以及应用。

Logic Inference in Bayesian Network Based on Conditional Event Algebra

We have described a relatively new logic system named Conditional Event Algebra(CEA) which has the important foreground in the data fusion system.It can solve the problem of uncertainty,probability and illegibility.CEA rigorously extends standard probability theory to include events which are contingent such as rules and conditions.In the logic system,the "if ... then ..." is modeled as Boolean elements,and yet compatible with conditional probability quantitative value.For some special Bayesian Belief Network such as polytree network has had some feasible arithmetic of probability inference,but up to now,there are not feasible arithmetic of logic inference.We need the arithmetic of logic inference very much as the development of study of uncertainty knowledge.This paper shows the definition and basic property of product space conditional event algebra,brings forward the arithmetic of logic inference based on product conditional event algebra and the application of this arithmetic.