Fuzzy order-sorted feature logic

TL;DR

This paper extends order-sorted feature logic to a fuzzy setting, enabling more flexible reasoning with uncertain or imprecise information in knowledge representation.

Contribution

It introduces a fuzzy subsumption relation and semantics for OSF logic, generalizing previous crisp subsumption to handle fuzzy sets and degrees.

Findings

Defined a fuzzy subsumption relation generalizing Zadeh's inclusion.

Proved the fuzzy subsumption forms a partial order.

Developed algorithms for unification and subsumption degree computation.

Abstract

Order-Sorted Feature (OSF) logic is a knowledge representation and reasoning language based on function-denoting feature symbols and set-denoting sort symbols ordered in a subsumption lattice. OSF logic allows the construction of record-like terms that represent classes of entities and that are themselves ordered in a subsumption relation. The unification algorithm for such structures provides an efficient calculus of type subsumption, which has been applied in computational linguistics and implemented in constraint logic programming languages such as LOGIN and LIFE and automated reasoners such as CEDAR. This work generalizes OSF logic to a fuzzy setting. We give a flexible definition of a fuzzy subsumption relation which generalizes Zadeh's inclusion between fuzzy sets. Based on this definition we define a fuzzy semantics of OSF logic where sort symbols and OSF terms denote fuzzy sets. We extend the subsumption relation to OSF terms and prove that it constitutes a fuzzy partial order with the property that two OSF terms are subsumed by one another in the crisp sense if and only if their subsumption degree is greater than 0. We show how to find the greatest lower bound of two OSF terms by unifying them and how to compute the subsumption degree between two OSF terms, and we provide the complexity of these operations.