Hybrid Knowledge Bases based on Lifschitz's logic of Minimal Knowledge with Negation as Failure are a successful approach to combine the expressivity of Description Logics and Logic Programming in a single language. Their syntax, defined by Motik and Rosati, disallows function symbols. In order to define a well-founded semantics for MKNF HKBs, Knorr et al. define a partition of the modal atoms occurring in it, called the alternating fixpoint partition. In this paper, we propose an iterated fixpoint semantics for HKBs with function symbols. We prove that our semantics extends Knorr et al.'s, in that, for a function-free HKBs, it coincides with its alternating fixpoint partition. The proposed semantics lends itself well to a probabilistic extension with a distribution semantic approach, which is the subject of future work.

In Proceedings ICLP 2022, arXiv:2208.02685