Imprecise probabilistic query answering using measures of ignorance and degree of satisfaction
Imprecise probabilistic query answering using measures of ignorance and degree of satisfaction
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DOI：
10.1007/s10472-012-9286-x
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发表时间：
2012-03
影响因子：
1.2
通讯作者：
Anbu Yue;Weiru Liu;A. Hunter
中科院分区：
文献类型：
--
作者：
Anbu Yue;Weiru Liu;A. Hunter
在条件概率逻辑规划中，给定一个查询，回答查询的两种最常见的形式是概率区间或使用最大熵原理获得的精确概率。前者可以是非信息性的（例如，区间[0,1]），当先验知识不精确时，后者的可靠性是值得怀疑的。为了解决这个问题，在本文中，我们提出了一些方法来定量测量一个概率区间或单个概率是否足以回答一个查询。我们首先提出了一种方法来测量概率逻辑程序对查询的无知程度。无知的度量（w.r.t.查询）反映了查询的精确概率的可靠性，无知的高值表明单个概率不适合查询。然后，我们提出了一种方法来测量查询在给定区间内的确切概率，例如，二阶概率。我们称之为满意程度。如果查询完成后的满意度足够高，则可以接受给定的间隔作为查询的答案。我们还证明了我们的度量满足许多性质，并通过一个案例来说明度量的意义。
In conditional probabilistic logic programming, given a query, the two most common forms for answering the query are either a probability interval or a precise probability obtained by using the maximum entropy principle. The former can be noninformative (e.g., interval [0, 1]) and the reliability of the latter is questionable when the priori knowledge is imprecise. To address this problem, in this paper, we propose some methods to quantitatively measure if a probability interval or a single probability is sufficient for answering a query. We first propose an approach to measuring the ignorance of a probabilistic logic program with respect to a query. The measure of ignorance (w.r.t. a query) reflects how reliable a precise probability for the query can be and a high value of ignorance suggests that a single probability is not suitable for the query. We then propose a method to measure the probability that the exact probability of a query falls in a given interval, e.g., a second order probability. We call it the degree of satisfaction. If the degree of satisfaction is high enough w.r.t. the query, then the given interval can be accepted as the answer to the query. We also prove our measures satisfy many properties and we use a case study to demonstrate the significance of the measures.