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Semi-qualitative Reasoning about Distances: A Preliminary Report

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Logics in Artificial Intelligence (JELIA 2000)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1919))

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Abstract

We introduce a family of languages intended for representing knowledge and reasoning about metric (and more general distance) spaces. While the simplest language can speak only about distances between individual objects and Boolean relations between sets, the more expressive ones are capable of capturing notions such as ‘somewhere in (or somewhere out of) the sphere of a certain radius’, ‘everywhere in a certain ring’, etc. The computational complexity of the satisfiability problem for formulas in our languages ranges from NP-completeness to undecidability and depends on the class of distance spaces in which they are interpreted. Besides the class of all metric spaces, we consider, for example, the spaces ℝ × ℝ and ℕ × ℕ with their natural metrics.

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Author information

Authors and Affiliations

  1. Institut für Informatik, Universität Leipzig, Augustus-Platz 10-11, 04109, Leipzig, Germany

    Holger Sturm & Nobu-Yuki Suzuki

  2. Department of Mathematics, Faculty of Science, Shizuoka University, Ohya 836, Shizuoka, 422-8529, Japan

    Frank Wolter

  3. Division of Artificial Intelligence, School of Computer Studies University of Leeds, Leeds, LS2 9JT, UK

    Michael Zakharyaschev

Authors
  1. Holger Sturm
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  2. Nobu-Yuki Suzuki
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  3. Frank Wolter
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  4. Michael Zakharyaschev
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Editor information

Editors and Affiliations

  1. Department of Applied Mathematics, E.T.S.I. Informática, University of Málaga, 29071, Málaga, Spain

    Manuel Ojeda-Aciego  & Inma P. de Guzmán  & 

  2. Intelligent Systems Department, Computer Science Institute, University of Leipzig, Augustusplatz 10-11, 04109, Leipzig, Germany

    Gerhard Brewka

  3. Center for Artificial Intelligence, Department of Computer Science, University of Lisbon, 2825-114, Caparica, Portugal

    Luís Moniz Pereira

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© 2000 Springer-Verlag Berlin Heidelberg

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Sturm, H., Suzuki, NY., Wolter, F., Zakharyaschev, M. (2000). Semi-qualitative Reasoning about Distances: A Preliminary Report. In: Ojeda-Aciego, M., de Guzmán, I.P., Brewka, G., Moniz Pereira, L. (eds) Logics in Artificial Intelligence. JELIA 2000. Lecture Notes in Computer Science(), vol 1919. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-40006-0_4

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  • DOI: https://doi.org/10.1007/3-540-40006-0_4

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41131-4

  • Online ISBN: 978-3-540-40006-6

  • eBook Packages: Springer Book Archive

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