Stable Model Semantics for Probabilistic Deductive Databases

In this paper we study the uses and the semantics of non-monotonic negation in probabilistic deductive databases. Based on the stable model semantics for classical logic programming, we examine two notions of stability. The first one is stable probabilistic models which are straightforward extensions of the classical stable models. But we prove that this notion may be too weak in our probabilistic framework. Then we introduce the second notion: stable families of probabilistic models. We show that this notion is much stronger than the first one, and we demonstrate how this stable family semantics can handle default reasoning appropriately in the context of probabilistic deduction.