Complexity of Conservative Extensions and Inseparability in the Description Logic \({\mathcal {EL}}^\lnot \)

  • Yuming ShenEmail author
  • Ju Wang
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 480)


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 \({\mathcal {EL}}^\lnot .\)


Ontology Conservative extension Computational complexity 



The work was supported by the National Natural Science Foundation of China under Grant Nos.60573010, 61103169.


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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Cisco School of InformaticsGuangdong University of Foreign StudiesGuangzhouChina
  2. 2.School of Computer Science and Information EngineeringGuangxi Normal UniversityGuilinChina

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