Revising Imprecise Probabilistic Beliefs in the Framework of Probabilistic Logic Programming

Probabilistic logic programming is a powerful technique to represent and reason with imprecise probabilistic knowledge. A probabilistic logic program (PLP) is a knowledge base which contains a set of conditional events with probability intervals. In this paper, we investigate the issue of revising such a PLP in light of receiving new information. We propose postulates for revising PLPs when a new piece of evidence is also a probabilistic conditional event. Our postulates lead to Jeffrey’s rule and Bayesian conditioning when the original PLP defines a single probability distribution. Furthermore, we prove that our postulates are extensions to Darwiche and Pearl (DP) postulates when new evidence is a propositional formula. We also give the representation theorem for the postulates and provide an instantiation of revision operators satisfying the proposed postulates.