Towards the Theory of Relaxed Unification

Classical unification is strict in the sense that it requires a perfect agreement between the terms being unified. In practice, data is seldom error-free and can contain inconsistent information. Classical unification fails when the data is imperfect. Fuzzy unification partially addresses uncertainty but requires the creation of fuzzy databases. We propose the Theory of Relaxed Unification as a new theory that relaxes the constraints of classical unification without requiring special pre-processing of data. The goal of relaxed unification is to tolerate possible errors and inconsistencies in the data and facilitate reasoning under uncertainty. The Theory of Relaxed Unification is more general and has higher expressive power than the classical Theory of Unification. We present the fundamental concepts of relaxed unification, a relaxed unification algorithm, and a number of examples.