Three-Valued Semantics for Hybrid MKNF Knowledge Bases Revisited (Extended Abstract)

Three-Valued Semantics for Hybrid MKNF Knowledge Bases Revisited (Extended Abstract)

Fangfang Liu, Jia-Huai You

Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence
Journal track. Pages 5627-5631. https://doi.org/10.24963/ijcai.2018/798

Knorr et al. (2011) formulated a three-valued formalism for the logic of Minimal Knowledge and Negation as Failure (MKNF) and proposed a well-founded semantics for hybrid MKNF knowledge bases (KBs). The main results state that if a hybrid MKNF KB has a three-valued MKNF model, its well-founded MKNF model exists, which is unique and can be computed by an alternating fixpoint construction. In this paper, we show that these claims are erroneous. We propose a classification of hybrid MKNF KBs into a hierarchy and show that its innermost subclass is what works for the well-founded semantics of Knorr et al. Furthermore, we provide a uniform characterization of well-founded, two-valued, and all three-valued MKNF models, in terms of stable partitions and the alternating fixpoint construction, which leads to updated complexity results as well as proof-theoretic tools for reasoning under these semantics.
Keywords:
Knowledge Representation and Reasoning: Logics for Knowledge Representation
Knowledge Representation and Reasoning: Knowledge Representation Languages
Knowledge Representation and Reasoning: Non-monotonic Reasoning
Knowledge Representation and Reasoning: Description Logics and Ontologies