An Iterative Fixpoint Semantics for MKNF Hybrid Knowledge Bases with Function Symbols

Marco Alberti
(Dipartimento di Matematica e Informatica, University of Ferrara)
Riccardo Zese
(Dipartimento di Scienze Chimiche, Farmaceutiche ed Agrarie, University of Ferrara)
Fabrizio Riguzzi
(Dipartimento di Matematica e Informatica, University of Ferrara)
Evelina Lamma
(Dipartimento di Ingegneria, University of Ferrara)

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 Yuliya Lierler, Jose F. Morales, Carmine Dodaro, Veronica Dahl, Martin Gebser and Tuncay Tekle: Proceedings 38th International Conference on Logic Programming (ICLP 2022), Haifa, Israel, 31st July 2022 - 6th August 2022, Electronic Proceedings in Theoretical Computer Science 364, pp. 65–78.
Published: 4th August 2022.

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