A semantics for probabilistic hybrid knowledge bases with function symbols

Hybrid Knowledge Bases (HKBs) successfully integrate Logic Programming (LP) and Description Logics (DL) under the Minimal Knowledge with Negation as Failure semantics. Both world closure assumptions (open and closed) can be used in the same HKB, a feature required in many domains, such as the legal and health-care ones. In previous work, we proposed (function-free) Probabilistic HKBs, whose semantics applied Sato's distribution semantics approach to the well-founded HKB semantics proposed by Knorr et al. and Lyu and You. This semantics relied on the fact that the grounding of a function-free Probabilistic HKB (PHKB) is finite. In this article, we extend the PHKB language to allow function symbols, obtaining PHKBFS. Because the grounding of a PHKBFS can be infinite, we propose a novel semantics which does not require the PHKBFS's grounding to be finite. We show that the proposed semantics extends the previously proposed semantics and that, for a large class of PHKBFS, every query can be assigned a probability.