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Inseparability and Conservative Extensions of Description Logic Ontologies: A Survey

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Reasoning Web: Logical Foundation of Knowledge Graph Construction and Query Answering (Reasoning Web 2016)

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Abstract

The question whether an ontology can safely be replaced by another, possibly simpler, one is fundamental for many ontology engineering and maintenance tasks. It underpins, for example, ontology versioning, ontology modularization, forgetting, and knowledge exchange. What ‘safe replacement’ means depends on the intended application of the ontology. If, for example, it is used to query data, then the answers to any relevant ontology-mediated query should be the same over any relevant data set; if, in contrast, the ontology is used for conceptual reasoning, then the entailed subsumptions between concept expressions should coincide. This gives rise to different notions of ontology inseparability such as query inseparability and concept inseparability, which generalize corresponding notions of conservative extensions. In this chapter, we survey results on various notions of inseparability in the context of description logic ontologies, discussing their applications, useful model-theoretic characterizations, algorithms for determining whether two ontologies are inseparable (and, sometimes, for computing the difference between them if they are not), and the computational complexity of this problem.

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Notes

  1. 1.

    http://www.ihtsdo.org/snomed-ct.

  2. 2.

    For DLs that admit role inclusions, one additionally considers entailment of these.

  3. 3.

    An alternative elementary proof is given in [52].

  4. 4.

    This should not be confused with the size of uniform interpolants, which can even be triple exponential in \(\mathcal{EL}\) [54].

  5. 5.

    Similar robustness properties and notions of equivalence have been discussed in logic programming, we refer the reader to [69,70,71] and references therein. We will discuss this robustness property further in Sect. 8.

  6. 6.

    In fact, when we say ‘Horn DL’, we mean a DL in which every KB has a universal model.

  7. 7.

    \(\mathcal {I} _2'\) is a subinterpretation of \(\mathcal {I} _2\) if \(\varDelta ^{\smash {\mathcal {I} '_2}} \subseteq \varDelta ^{\smash {\mathcal {I} _2}}\), \(A^{\smash {\mathcal {I} '_2}} = A^{\smash {\mathcal {I} _2}} \cap \varDelta ^{\smash {\mathcal {I} '_2}}\) and \(r^{\smash {\mathcal {I} '_2}} = r^{\smash {\mathcal {I} _2}} \cap (\varDelta ^{\smash {\mathcal {I} '_2}} \times \varDelta ^{\smash {\mathcal {I} '_2}})\), for all concept names A and role names r.

  8. 8.

    Robustness under replacement can be defined for KBs as well and is equally important in that case. In this short discussion, however, we only consider TBox inseparability.

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Acknowledgments

Elena Botoeva was supported by EU IP project Optique, grant n. FP7-318338. Carsten Lutz was supported by ERC grant 647289. Boris Konev, Frank Wolter and Michael Zakharyaschev were supported by the UK EPSRC grants EP/M012646, EP/M012670, EP/H043594, and EP/H05099X.

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Authors and Affiliations

  1. Faculty of Computer Science, Free University of Bozen-Bolzano, Bolzano, Italy

    Elena Botoeva & Vladislav Ryzhikov

  2. Department of Computer Science, University of Liverpool, Liverpool, UK

    Boris Konev & Frank Wolter

  3. Faculty of Informatics, University of Bremen, Bremen, Germany

    Carsten Lutz

  4. Department of Computer Science and Information Systems, Birkbeck University of London, London, UK

    Michael Zakharyaschev

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  1. Elena Botoeva
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  2. Boris Konev
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  4. Vladislav Ryzhikov
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  5. Frank Wolter
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  6. Michael Zakharyaschev
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Correspondence to Frank Wolter .

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Editors and Affiliations

  1. University of Aberdeen , Aberdeen, United Kingdom

    Jeff Z. Pan

  2. Free University of Bozen-Bolzano , Bolzano, Italy

    Diego Calvanese

  3. University of Technology Vienna , Vienna, Austria

    Thomas Eiter

  4. University of Oxford , Oxford, United Kingdom

    Ian Horrocks

  5. Stony Brook University , Stony Brook, New York, USA

    Michael Kifer

  6. University of Science and Technology , Hong Kong, China

    Fangzhen Lin

  7. University of Aberdeen , Aberdeen, United Kingdom

    Yuting Zhao

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Botoeva, E., Konev, B., Lutz, C., Ryzhikov, V., Wolter, F., Zakharyaschev, M. (2017). Inseparability and Conservative Extensions of Description Logic Ontologies: A Survey. In: Pan, J., et al. Reasoning Web: Logical Foundation of Knowledge Graph Construction and Query Answering. Reasoning Web 2016. Lecture Notes in Computer Science(), vol 9885. Springer, Cham. https://doi.org/10.1007/978-3-319-49493-7_2

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