Order-Sorted Quantified Modal Logic: Tableau Calculus and Ontological Property Classification

The notions of meta-ontology enhance the ability to process knowledge in informa-tion systems; in particular, ontological property classification deals with the kinds ofproperties in taxonomic knowledge based on a philosophical analysis. The goal of thispaper is to devise a reasoning mechanism to check the ontological and logical consistencyof knowledge bases, which is important for reasoning services on taxonomic knowledge.We first consider an ontological property classification that is extended to capture in-dividual existence and time and situation dependencies. To incorporate the notioninto logical reasoning, we formalize an order-sorted modal logic that involves rigidity,sortality, and three kinds of modal operators (temporal/situational/any world). Thesorted expressions and modalities establish axioms with respect to properties, implyingthe truth of properties in different kinds of possible worlds and in varying domains inKripke semantics. We provide a prefixed tableau calculus to test the satisfiability ofsuch sorted modal formulas, which validates the ontological axioms of properties.