Inconsistency-tolerant reasoning over linear probabilistic knowledge bases

We consider the problem of reasoning under uncertainty in the presence of inconsistencies. Our knowledge bases consist of linear probabilistic constraints that, in particular, generalize many probabilistic-logical knowledge representation formalisms. We first generalize classical probabilistic models to inconsistent knowledge bases by considering a notion of minimal violation of knowledge bases. Subsequently, we use these generalized models to extend two classical probabilistic reasoning problems (the probabilistic entailment problem and the model selection problem) to inconsistent knowledge bases. We show that our approach satisfies several desirable properties and discuss some of its computational properties.