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Towards Constructive DL for Abstraction and Refinement

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Abstract

This work explores some aspects of a new and natural semantical dimension that can be accommodated within the syntax of description logics which opens up when passing from the classical truth-value interpretation to a constructive interpretation. We argue that such a strengthened interpretation is essential to represent applications with partial information adequately and to achieve consistency under abstraction as well as robustness under refinement. We introduce a constructive version of \(\mathcal{ALC}\), called \({c\mathcal{ALC}}\), for which we give a sound and complete Hilbert axiomatisation and a Gentzen tableau calculus showing finite model property and decidability.

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Authors and Affiliations

  1. Faculty of Information Systems and Applied Computer Sciences, The Otto-Friedrich-University of Bamberg, Bamberg, Germany

    Michael Mendler & Stephan Scheele

Authors
  1. Michael Mendler
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  2. Stephan Scheele
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Correspondence to Stephan Scheele.

Additional information

An extended abstract of this work has been presented at the 21th International Workshop on Description Logics (DL2008).

This work is funded by the German Research Council (DFG) as part of the project SPACMODL grant No. ME 1427/4-1.

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Mendler, M., Scheele, S. Towards Constructive DL for Abstraction and Refinement. J Autom Reasoning 44, 207–243 (2010). https://doi.org/10.1007/s10817-009-9151-8

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  • DOI: https://doi.org/10.1007/s10817-009-9151-8

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