Abstract
The notations of conservative extensions and inseparability are suggested as the effective tool for comparing, merging, and modularizing description logic ontologies. It has been shown that the complexity of conservative extensions for expressive descriptions logics such as \({\mathcal {ALC}}\) and \({\mathcal {ALCQI}}\) are 2ExpTime-complete and ExpTime-complete for \({\mathcal {EL}}\) itself. However, the problem of the complexity of conservative extensions in a few extensions of \({\mathcal {EL}}\) which used in applications has hardly been addressed. The aim of this paper is to study the complexity of conservative extensions and inseparability in the description logic \({\mathcal {EL}}^\lnot ,\) which is the extension of \({\mathcal {EL}}\) with atomic concept negation. By adding many countable new concept names which correspond to the complex negative concepts, we establish a translation from \({\mathcal {ALC}}\) to \({\mathcal {EL}}^\lnot \) and reduce the problem of conservative extensions in \({\mathcal {ALC}}\) to the case of \({\mathcal {EL}}^\lnot .\) Since deciding conservative extensions and inseparability in \({\mathcal {ALC}}\) is 2ExpTime-complete, we get 2ExpTime-completeness of both inseparability and conservative extensions in \({\mathcal {EL}}^\lnot .\)
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The work was supported by the National Natural Science Foundation of China under Grant Nos.60573010, 61103169.
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Shen, Y., Wang, J. (2014). Complexity of Conservative Extensions and Inseparability in the Description Logic \({\mathcal {EL}}^\lnot \) . In: Zhao, D., Du, J., Wang, H., Wang, P., Ji, D., Pan, J. (eds) The Semantic Web and Web Science. CSWS 2014. Communications in Computer and Information Science, vol 480. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45495-4_7
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