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 \(\mathcal {FL}_0\), 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 \(\mathcal {FL}_0\) can be reduced to approximately solving language equations, and devise algorithms for solving the latter problem for two particular distance measures.
F. Baader—Supported by the Cluster of Excellence ‘Center for Advancing Electronics Dresden’.
P. Marantidis—Supported by DFG Graduiertenkolleg 1763 (QuantLA).
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Notes
- 1.
In the first line below we assume, as usual, that \(\min \emptyset = \infty \) and \(2^{-\infty } = 0\).
- 2.
An ILTA \((\varSigma , Q, Q_0, \delta )\) is trim if every state is reachable from an initial state and \(\delta (q,a) \ne \emptyset \) for all \(q\in Q, a\in \varSigma \).
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Baader, F., Marantidis, P., Okhotin, A. (2016). Approximate Unification in the Description Logic \(\mathcal {FL}_0\) . In: Michael, L., Kakas, A. (eds) Logics in Artificial Intelligence. JELIA 2016. Lecture Notes in Computer Science(), vol 10021. Springer, Cham. https://doi.org/10.1007/978-3-319-48758-8_4
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