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Specifying Well-Formed Part-Whole Relations in Coq

  • Conference paper
Graph-Based Representation and Reasoning (ICCS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8577))

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Abstract

In the domain of ontology design as well as in Conceptual Modeling, representing part-whole relations is a long-standing challenging problem. However, in most papers the focus has been on properties of the part-whole relation, rather than on its semantics. In the last decades, most approaches which have addressed the formal specification of the part-whole relation (i) rely on First Order Logic (FOL) which is unable to address multiple levels of granularity and (ii) do not support any typing mechanism useful for the extensional side of concepts and then, many difficulties remain especially about expressiveness. In mathematical logic and program checking, type theories have proved to be appealing but so far, they have not been applied in the formalization of ontological relations. To bridge this gap, we present an axiomatization of the part-whole relation which hold between typed terms. Relation structures in the dependently-typed framework rely on a constructive logic. We define in a precise way what relation structures and their meta-properties, are in term of type classes using the Coq language.

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Authors and Affiliations

  1. LISTIC/Polytech’Annecy-Chambéry, University of Savoie, Po. Box 80439, 74944, Annecy-le-vieux Cedex, France

    Richard Dapoigny & Patrick Barlatier

Authors
  1. Richard Dapoigny
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  2. Patrick Barlatier
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Correspondence to Richard Dapoigny .

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Editors and Affiliations

  1. Université Toulouse le Mirail, Toulouse, France

    Nathalie Hernandez

  2. L3S Research Center, Hannover, Germany

    Robert Jäschke

  3. LIRMM, Montpellier, France

    Madalina Croitoru

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Dapoigny, R., Barlatier, P. (2014). Specifying Well-Formed Part-Whole Relations in Coq. In: Hernandez, N., Jäschke, R., Croitoru, M. (eds) Graph-Based Representation and Reasoning. ICCS 2014. Lecture Notes in Computer Science(), vol 8577. Springer, Cham. https://doi.org/10.1007/978-3-319-08389-6_14

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  • DOI: https://doi.org/10.1007/978-3-319-08389-6_14

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08388-9

  • Online ISBN: 978-3-319-08389-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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