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Matching concept descriptions against concept patterns was introduced as a new inference task in Description Logics two decades ago, motivated by applications in the Classic system. Shortly afterwards, a polynomial-time matching algorithm was developed for the DL FL0. However, this algorithm cannot deal with general TBoxes (i.e., finite sets of general concept inclusions). Here we show that matching in FL0 w.r.t. general TBoxes is in ExpTime, which is the best possible complexity for this problem since already subsumption w.r.t. general TBoxes is ExpTime-hard in FL0. We also show that, w.r.t. a restricted form of TBoxes, the complexity of matching in FL0 can be lowered to PSpace.

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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.