Measuring the Ignorance and Degree of Satisfaction for Answering Queries in Imprecise Probabilistic Logic Programs

Authors:
Anbu Yue;Weiru Liu;Anthony Hunter
Affiliations:
School of Electronics, Electrical Engineering and Computer Science, Queen's University Belfast, Belfast, UK BT7 1NN;School of Electronics, Electrical Engineering and Computer Science, Queen's University Belfast, Belfast, UK BT7 1NN;Department of Computer Science, University College London, London, UK WC1E 6BT
Venue:
SUM '08 Proceedings of the 2nd international conference on Scalable Uncertainty Management
Year:
2008

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Abstract

In probabilistic logic programming, given a query, either a probability interval or a precise probability obtained by using the maximum entropy principle is returned for the query. 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 provide properties of the two measures and use an example to demonstrate the significance of the measures.