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What Is a Qualitative Calculus? A General Framework

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PRICAI 2004: Trends in Artificial Intelligence (PRICAI 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3157))

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Abstract

What is a qualitative calculus? Many qualitative spatial and temporal calculi arise from a set of JEPD (jointly exhaustive and pairwise disjoint) relations: a stock example is Allen’s calculus, which is based on thirteen basic relations between intervals on the time line. This paper examines the construction of such a formalism from a general point of view, in order to make apparent the formal algebraic properties of all formalisms of that type. We show that the natural algebraic object governing this kind of calculus is a non-associative algebra (in the sense of Maddux), and that the notion of weak representation is the right notion for describing most basic properties. We discuss the ubiquity of weak representations in various guises, and argue that the fundamental notion of consistency itself can best be understood in terms of consistency of one weak representation with respect to another.

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Author information

Authors and Affiliations

  1. LIMSI-CNRS, Université Paris-Sud, 91403, Orsay, France

    Gérard Ligozat

  2. National ICT Australia, Knowledge Representation and Reasoning Group, UNSW Sydney, NSW 2052, Australia

    Jochen Renz

Authors
  1. Gérard Ligozat
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  2. Jochen Renz
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Editor information

Editors and Affiliations

  1. Faculty of Engineering and Information Technology, Centre for Quantum Computation and Intelligent Systems, and Australian ACS National Committee for Artificial Intelligence, University of Technology, Sydney, Australia

    Chengqi Zhang

  2. Department of Computer Science, Auckland University of Technology, 1020, Auckland, New Zealand

    Hans W. Guesgen

  3. Artificial Intelligence Technology Centre, Auckland University of Technology, Auckland, New Zealand

    Wai-Kiang Yeap

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Ligozat, G., Renz, J. (2004). What Is a Qualitative Calculus? A General Framework. In: Zhang, C., W. Guesgen, H., Yeap, WK. (eds) PRICAI 2004: Trends in Artificial Intelligence. PRICAI 2004. Lecture Notes in Computer Science(), vol 3157. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28633-2_8

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  • DOI: https://doi.org/10.1007/978-3-540-28633-2_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22817-2

  • Online ISBN: 978-3-540-28633-2

  • eBook Packages: Springer Book Archive

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