Probabilistic Reasoning with Inconsistent Beliefs Using Inconsistency Measures / 3156
Nico Potyka, Matthias Thimm
PDF

The classical probabilistic entailment problem is to determine upper and lower bounds on the probability of formulas, given a consistent set of probabilistic assertions. We generalize this problem by omitting the consistency assumption and, thus, provide a general framework for probabilistic reasoning under inconsistency. To do so, we utilize inconsistency measures to determine probability functions that are closest to satisfying the knowledge base. We illustrate our approach on several examples and show that it has both nice formal and computational properties.