Approximate Unification in the Description Logic FL₀

Abstract

Unification in description logics (DLs) has been introduced as a novel inference service that can be used to detect redundancies in ontologies, by finding different concepts that may potentially stand for the same intuitive notion. It was first investigated in detail for the DL FL₀, where unification can be reduced to solving certain language equations. In order to increase the recall of this method for finding redundancies, we introduce and investigate the notion of approximate unification, which basically finds pairs of concepts that “almost” unify. The meaning of “almost” is formalized using distance measures between concepts. We show that approximate unification in FL₀ can be reduced to approximately solving language equations, and devise algorithms for solving the latter problem for two particular distance measures.

Remarks about the unification types of some locally tabular normal modal logics

“…As is well-known, the unification type of FL 0 is nullary [5]. Restricting the discussion to the class of all 2-bounded ACT-frames, Baader et al [2] have proved that the unification type of FL 0 is unitary. This leads us to the following open questions:…”