Ontological Knowledge Base Reasoning with Sort-Hierarchy and Rigidity

Although sorts and unary predicates are semantically identical in order-sorted logic, they are classified as different kinds of properties in formal ontology (e.g. sortal and non-sortal). This ontological analysis is an essential notion to deal with properties (or sorts) of objects in knowledge representation and reasoning. In this paper, we propose an extension of an order-sorted logic with the ontological property classification. This logic contains types (rigid sorts), non-rigid sorts and unary predicates to distinguishably express the properties: substantial sorts, non-substantial sorts and non-sortal properties. We define a sorted Horn-clause calculus for such property expressions in a knowledge base. Based on the calculus, we develop a reasoning algorithm for many separated knowledge bases where each knowledge base can extract rigid property information from other knowledge bases (called rigid property derivation).