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Tableau-Based Reasoning

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Handbook on Ontologies

Part of the book series: International Handbooks on Information Systems ((INFOSYS))

Summary

Tableau-based methods for satisfiability checking build the backbone of major contemporary ontology reasoning sytems. The main idea of tableau-based methods for satisfiability checking is to systematically construct a representation for a model of the input formulae. If all representations that are considered by the procedure turn out to contain an obvious contradiction, a model representation cannot be found and it is concluded that the set of formulae is unsatisfiable.

In this chapter, tableau-based reasoning methods are formally introduced. We start with a nondeterministic basic version which subsequently will be extended with optimization techniques in order to demonstrate how practical systems can be built. We also demonstrate how computed tableau structures can be exploited for other inference problems in an ontology reasoning system.

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Notes

  1. 1.

    For instance, if numbers are chosen for the unique identifier, the unique identifier of the negation of a (non-negated) concept with number n could be n + 1. The encoding process must assign numbers accordingly. If (pointers to) objects are used for representing concepts, a field with a pointer to the negated concept provides for a fast implementation of neg at the cost of memory requirements probably being a little bit higher.

  2. 2.

    We use a way to construct the canonical interpretation that already considers additional concept constructors such as, say, number restrictions. In case of \(\mathcal {A}\mathcal {L}\mathcal {C}\) it would be possible to map i to its witness w in the canonical interpretation.

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Acknowledgments

We would like to thank Sebastian Wandelt and Michael Wessel for comments on a draft of this chapter.

Author information

Authors and Affiliations

  1. Hamburg University of Technology, Hamburg, Germany

    Ralf Möller

  2. Concordia University, Montreal, Canada

    Volker Haarslev

Authors
  1. Ralf Möller
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  2. Volker Haarslev
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Correspondence to Ralf Möller .

Editor information

Editors and Affiliations

  1. Inst. Informatik, Universität Koblenz-Landau, Universitaetsstr. 1, Koblenz, 56016, Germany

    Steffen Staab

  2. Inst. Angewandte Informatik und, Universität Karlsruhe, Karlsruhe, 76128, Germany

    Rudi Studer

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Möller, R., Haarslev, V. (2009). Tableau-Based Reasoning. In: Staab, S., Studer, R. (eds) Handbook on Ontologies. International Handbooks on Information Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92673-3_23

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  • DOI: https://doi.org/10.1007/978-3-540-92673-3_23

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  • Print ISBN: 978-3-540-70999-2

  • Online ISBN: 978-3-540-92673-3

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