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Distributed reasoning with coupled ontologies: the \(E\text {-}{\mathcal {SHIQ}}\) representation framework

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Abstract

Combining ontologies in expressive fragments of Description Logics in inherently distributed peer-to-peer settings with autonomous peers is still a challenge in the general case. Although several modular ontology representation frameworks have been proposed for combining Description Logics knowledge bases, each of them has its own strengths and limitations. In this paper, we consider networks of peers, where each peer holds its own ontology within the \({\mathcal {SHIQ}}\) fragment of Description Logics, and subjective beliefs on how its knowledge can be coupled with the knowledge of others. To allow peers to reason jointly with their coupled knowledge, while preserving their autonomy on evolving their knowledge, data, and subjective beliefs, we propose the \(E\text {-}{\mathcal {SHIQ}}\) representation framework. The article motivates the need for \(E\text {-}{\mathcal {SHIQ}}\) and compares it to existing representation frameworks for modular Description Logics. It discusses the implementation of the \(E\text {-}{\mathcal {SHIQ}}\) distributed reasoner and presents experimental results on the efficiency of this reasoner.

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Notes

  1. http://clarkparsia.com/pellet/.

  2. Other types of mappings between ontology elements [8, 9] are beyond the scope of this work.

  3. http://hermit-reasoner.com/.

  4. MORe (http://www.cs.ox.ac.uk/isg/tools/MORe/) is a state-of-the-art concept classification optimization method that partitions the ontology into a part of low expressiveness and a—usually—smaller part of high expressiveness. Inferences from the smaller part are propagated accordingly to the larger part. MORe benefits from using a polynomial reasoner for the larger part of low expressiveness.

  5. This is a soft form of an agreement: (a) correspondences between some units may coincide but involved units do not necessarily know it (i.e., a unit does not know the correspondences of another), (b) if one of the involved units drops the correspondence, this action will not affect the symmetric correspondence of the other. Although there are means for units to reach consensus [32], these are not within the scope of this paper,

  6. To transform any concept into NNF, De Morgan’s laws are applied, as well as the duality between atmost and atleast number restrictions. In NNF, negation occurs in front of the concept names only.

  7. Complete proofs are publicly available online [34].

  8. Please notice that cases where \(i = j\) and \(i \ne j\) can be distinguished.

  9. A cyclic connection between units \(i\) and \(j\) may be due either to concept and/or individual correspondences from \(i\) to \(j\) and from \(j\) to \(i\), or to combinations between concept and/or individual correspondences from \(j\) to \(i\) and ij-link relations.

  10. Available at http://ai-group.ds.unipi.gr/ai-group/SISontologies.html.

  11. Available at http://ai-group.ds.unipi.gr/ai-group/ESHIQontologies.html.

  12. It is very difficult to show in a succinct way how projection requests propagate along paths in the network; thus, we aggregate all projections triggered by a peer to the entry for this peer.

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Acknowledgments

This research project is being supported by the project “IRAKLITOS II” of the O.P.E.L.L. 2007–2013 of the NSRF (2007–2013), co-funded by the European Union and National Resources of Greece.

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Authors and Affiliations

  1. Department of Information and Communications Systems Engineering, University of the Aegean, Karlovassi, Samos, Greece

    Georgios Santipantakis

  2. Department of Digital Systems, University of Piraeus, Karaoli and Dimitriou 80, Piraeus, Greece

    George A. Vouros

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  1. Georgios Santipantakis
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Correspondence to Georgios Santipantakis.

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Santipantakis, G., Vouros, G.A. Distributed reasoning with coupled ontologies: the \(E\text {-}{\mathcal {SHIQ}}\) representation framework. Knowl Inf Syst 45, 491–534 (2015). https://doi.org/10.1007/s10115-014-0807-2

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