Combining Order-Sorted Logic Programming with Formal Ontology

In formal ontology, entity types and relationships are philosophically defined, and the properties of objects are classified on the basis of sortality, rigidity, and identity (called property classification). Sorts and unary predicates are semantically identical in order-sorted logic, but they are respectively sortal and non-sortal (i.e., they are distinguished) in a formal ontology. This ontological distinction is essential for dealing with the properties (or sorts) of objects in knowledge representation and reasoning. In this paper, we propose an extension of an order-sorted logic with ontological property classification. This logic contains types (rigid sorts), anti-rigid sorts, and unary predicates to distinctly express the kinds of properties: essential sorts, non-essential sorts, and nonsortal properties. We formalize an order-sorted Horn-clause calculus for such property expressions in a knowledge base, and present a derivation system for many separated knowledge bases each of which can extract rigid-property information from other knowledge bases (called rigid-property derivation). To enable the reasoning mechanism to be utilized, we provide a query answering system that combines an order-sorted linear resolution system (as a top-down reasoning mechanism) and a rigid-property derivation system for many knowledge bases. keywords: ontological property classification, rigidity, order-sorted logic, knowledge base reasoning, linear resolution system