Approximating Linear Order Inference in OWL 2 DL by Horn Compilation

In order to directly reason over inconsistent OWL 2 DL ontologies, this paper considers linear order inference which comes from propositional logic. Consequences of this inference in an inconsistent ontology are defined as consequences in a certain consistent sub-ontology. This paper proposes a novel framework for compiling an OWL 2 DL ontology to a Horn propositional program so that the intended consistent sub-ontology for linear order inference can be approximated from the compiled result in polynomial time. A tractable method is proposed to realize this framework. It guarantees that the compiled result has a polynomial size. Experimental results show that the proposed method computes the exact intended sub-ontology for almost all test cases, while it is significantly more efficient and scalable than state-of-the-art exact methods.