Imprecise probabilistic query answering using measures of ignorance and degree of satisfaction

Anbu Yue, Weiru Liu, Anthony Hunter

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
241 Downloads (Pure)


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 isimprecise. To address this problem, in this paper, we propose some methods to quantitativelymeasure 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 howreliable 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 highenough 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. © Springer Science+Business Media B.V. 2012
Original languageEnglish
Pages (from-to)145-183
Number of pages39
JournalAnnals of Mathematics and Artificial Intelligence
Issue number2-3
Publication statusPublished - Mar 2012
EventInternational Conference on Scalable Uncertainty Management 2008 - Napoli, Italy
Duration: 01 Oct 200803 Oct 2008


  • Probabilistic logic programming
  • Queries
  • Ignorance
  • Imprecise probability


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