An Order-Sorted Quantified Modal Logic for Ontological Property Classification

In the field of ontology, several property classifications have been defined as meta-ontologies wherein the properties of individuals are rigorously classified as sortal/non-sortal, rigid/anti-rigid/non-rigid, etc. through philosophical analysis. The notions ofsuch meta-ontologies enable the processing of properties that allow us to reason abouttaxonomic knowledge in information systems. The goal of our research is to devise areasoning mechanism that verifies the ontological consistency of knowledge bases in ad-dition to their logical consistency. We first propose an ontological property classificationbased on individual existence and temporal and situational aspects of properties thatestablishes an infrastructure for knowledge bases. Second, by combining order-sortedlogic and quantified modal logic, we develop an order-sorted modal logic in order to in-corporate meta-ontologies into logical reasoning systems that involve rigidity, sortality,and three types of modal operators (temporal/situational/any-world). In the extendedlogic, sorted expressions and modalities suitably represent the ontological axioms ofproperties, which are interpreted in different types of possible worlds and in varyingdomains in Kripke semantics. As a reasoning system of the logic, we present a pre-fixed tableau calculus to test the satisfiability of sorted modal formulas including theontological property classification.