Similarity-Based Reasoning With Order-Sorted Feature Logic

Order-sorted feature (OSF) logic is a knowledge representation and reasoning language based on sorts—symbols that denote concepts ordered in a subsumption relation—and features—symbols that denote functional attributes. Reasoning with OSF logic is based on the unification of OSF terms, record-like structures that denote classes of objects and that are themselves ordered in a subsumption relation. OSF term unification aims to combine the constraints expressed by two terms in a consistent way, and it takes into account the subsumption relation between sort symbols, providing an efficient calculus of type subsumption. This article presents an approach to define approximate reasoning with OSF logic by extending its language with a similarity relation on sorts. In order for the OSF term unification algorithm to take into account this similarity and its interaction with the subsumption relation, we propose to combine the two relations into a single fuzzy subsumption relation. The advantage is that the same unification rules of OSF logic can then be applied to this fuzzy setting. We conclude by discussing potential applications of OSF logic extended with a sort similarity relation.