Interval-type and affine arithmetic-type techniques for handling uncertainty in expert systems
Interval-type and affine arithmetic-type techniques for handling uncertainty in expert systems
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DOI：
10.1016/j.cam.2005.08.030
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发表时间：
2007-02-15
影响因子：
2.4
通讯作者：
Baral, Chitta
中科院分区：
文献类型：
--
作者：
Ceberio, Martine;Kreinovich, Vladik;Baral, Chitta
专家知识由陈述S-j(事实和规则)组成。事实和规则往往只有在一定的概率下才是真实的。例如，如果我们对石油感兴趣，我们应该看看地震数据。如果在90%的情况下，地震数据确实有助于寻找石油，那么我们可以说，如果我们对石油感兴趣，那么90%的可能性是看地震数据是有帮助的。在更正式的术语中，我们可以说“如果石油那么地震”的含义有90%的可能性成立。另一个例子：银行A信任客户B，所以如果我们信任银行A，我们也应该信任B；如果从统计学上讲，99%的情况下这种信任是合理的，我们可以得出结论，相应的蕴含以99%的概率成立。如果一个查询Q可以从事实和规则中推导出来，那么得到的概率p(Q)在Q中是多少？我们可以用S公式F来描述Q的真实性，即由&、v和-等算符链接的语句S-j的组合；精确地计算p(Q)是NP困难的，因此需要启发式。传统上，专家系统使用类似于直接区间计算的技术：我们解析F，并用相应的概率运算来代替每一计算步骤。问题：在每一步，我们忽略了中间结果F-j之间的相关性；因此，区间太宽。例如：P(A，v-A)的估计不是1。解决方案：类似于仿射算法，除了P(F-j)外，我们还计算P(F-j&F-i)(或P(F-jl&中心点&F-jd))，在每一步，使用这些概率的所有组合来得到新的估计。结果：例如，P(A-A)估计为1。(C)2005 Elsevier B.V.保留所有权利。
Expert knowledge consists of statements S-j (facts and rules). The facts and rules are often only true with some probability. For example, if we are interested in oil, we should look at seismic data. If in 90% of the cases, the seismic data were indeed helpful in locating oil, then we can say that if we are interested in oil, then with probability 90% it is helpful to look at the seismic data. In more formal terms, we can say that the implication "if oil then seismic" holds with probability 90%. Another example: a bank A trusts a client B, so if we trust the bank A, we should trust B too; if statistically this trust was justified in 99% of the cases, we can conclude that the corresponding implication holds with probability 99%.If a query Q is deducible from facts and rules, what is the resulting probability p(Q) in Q? We can describe the truth of Q as a propositional formula F in terms of S-j, i.e., as a combination of statements S-j linked by operators like &, v, and -; computing p(Q) exactly is NP-hard, so heuristics are needed.Traditionally, expert systems use technique similar to straightforward interval computations: we parse F and replace each computation step with corresponding probability operation. Problem: at each step, we ignore the dependence between the intermediate results F-j; hence intervals are too wide. Example: the estimate for P(A v - A) is not 1. Solution: similar to affine arithmetic, besides P(F-j), we also compute P(F-j&F-i) (or P(F-jl ¢er dot center dot center dot & F-jd)), and on each step, use all combinations of 1 such probabilities to get new estimates. Results: e.g., P(A - A) is estimated as 1. (c) 2005 Elsevier B.V. All rights reserved.