A Distribution Semantics for non-DL-Safe Probabilistic Hybrid Knowledge Bases

Logic Programming languages and Description Logics are based on different domain closure assumptions, closed and the open world assumption, respectively. Since many domains require both these assumptions, the combination of LP and DL have become of foremost importance. An especially successful approach is based on Minimal Knowledge with Negation as Failure (MKNF), whose semantics is used to define Hybrid KBs, composed of logic programming rules and description logic axioms. Following such idea, we have proposed an approach for defining DL-safe Probabilistic Hybrid Knowledge Bases, where each disjunct in the head of LP clauses and each DL axiom is annotated with a probability value, following the well known distribution semantics. In this paper, we show that this semantics can be unintuitive for non-DL-safe PHKBs, and we propose a new semantics that coincides with the previous one if the PHKB is DL-safe.