# Well-Founded Operators for Normal Hybrid MKNF Knowledge Bases

arXiv: https://arxiv.org/abs/1707.01959 · HTML: https://mlsanity.com/paper/1707.01959/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jul 2017.

## Built on by (most cited first, 5 of 5)

- [Unfounded Sets for Disjunctive Hybrid MKNF Knowledge Bases](https://mlsanity.com/paper/2102.13162/) (2021)
- [Alternating Fixpoint Operator for Hybrid MKNF Knowledge Bases as an Approximator of AFT](https://mlsanity.com/paper/2105.11071/) (2021)
- [A Fixpoint Characterization of Three-Valued Disjunctive Hybrid MKNF Knowledge Bases](https://mlsanity.com/paper/2208.03087/) (2022)
- [On the Foundations of Conflict-Driven Solving for Hybrid MKNF Knowledge Bases](https://mlsanity.com/paper/2408.09626/) (2024)
- [Hybrid MKNF with Classical Negation in the Rule Component](https://mlsanity.com/paper/2607.21202/) (2026)

## Abstract (arXiv)

Hybrid MKNF knowledge bases have been considered one of the dominant approaches to combining open world ontology languages with closed world rule-based languages. Currently, the only known inference methods are based on the approach of guess-and-verify, while most modern SAT/ASP solvers are built under the DPLL architecture. The central impediment here is that it is not clear what constitutes a constraint propagator, a key component employed in any DPLL-based solver. In this paper, we address this problem by formulating the notion of unfounded sets for nondisjunctive hybrid MKNF knowledge bases, based on which we propose and study two new well-founded operators. We show that by employing a well-founded operator as a constraint propagator, a sound and complete DPLL search engine can be readily defined. We compare our approach with the operator based on the alternating fixpoint construction by Knorr et al [2011] and show that, when applied to arbitrary partial partitions, the new well-founded operators not only propagate more truth values but also circumvent the non-converging behavior of the latter. In addition, we study the possibility of simplifying a given hybrid MKNF knowledge base by employing a well-founded operator, and show that, out of the two operators proposed in this paper, the weaker one can be applied for this purpose and the stronger one cannot. These observations are useful in implementing a grounder for hybrid MKNF knowledge bases, which can be applied before the computation of MKNF models. The paper is under consideration for acceptance in TPLP.