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Towards an Ontological Modeling with Dependent Types: Application to Part-Whole Relations

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Conceptual Modeling - ER 2009 (ER 2009)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 5829))

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Abstract

Generally, mereological relations are modeled using fragments of first-order logic(FOL) and difficulties arise when meta-reasoning is done over their properties, leading to reason outside the logic. Alternatively, classical languages for conceptual modeling such as UML lack of formal foundations resulting in ambiguous interpretations of mereological relations. Moreover, they cannot prove that a given specification is correct from a logical perspective. In order to address all these problems, we suggest a formal framework using a dependent (higher-order) type theory such as those used in program checking and theorem provers (e.g., Coq). It is based on constructive logic and allows reasoning in different abstraction levels within the logic. Furthermore, it maximizes the expressiveness while preserving decidability of type checking and results in a coherent theory with a powerful sub-typing mechanism.

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Authors and Affiliations

  1. Laboratoire d’Informatique, Sytèmes, Traitement de l’Information et de la Connaissance, Université de Savoie, Po. Box 80439, 74944, Annecy-le-vieux cedex, France

    Richard Dapoigny & Patrick Barlatier

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  1. Richard Dapoigny
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  2. Patrick Barlatier
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Editors and Affiliations

  1. Department of Computer Science, Federal University of Minas Gerais, Av. Antônio Carlos 6627, Prédio do ICEx, sala 4010, Pampulha , Belo, 31270-901, Horizonte, MG, Brazil

    Alberto H. F. Laender

  2. Dipartimento di Scienze dell’Informazione, DICo, Università degli Studi di Milano, Comelico, 39/41, 20135, Milano, Italy

    Silvana Castano

  3. Hewlett-Packard Laboratories, 1501 Page Mill Rd., 94304, Palo Alto, CA, USA

    Umeshwar Dayal

  4. Department of Information Engineering and Computer Science, University of Trento, Via sommarive 14, 38050, Povo (Trento), Italy

    Fabio Casati

  5. Instituto de Informática, Universidade Federal do Rio Grande do Sul (UFRGS), Caixa Postal 15.064, 91.501-970, Porto Alegre, RS, Brasil

    José Palazzo M. de Oliveira

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Dapoigny, R., Barlatier, P. (2009). Towards an Ontological Modeling with Dependent Types: Application to Part-Whole Relations. In: Laender, A.H.F., Castano, S., Dayal, U., Casati, F., de Oliveira, J.P.M. (eds) Conceptual Modeling - ER 2009. ER 2009. Lecture Notes in Computer Science, vol 5829. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04840-1_13

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  • DOI: https://doi.org/10.1007/978-3-642-04840-1_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04839-5

  • Online ISBN: 978-3-642-04840-1

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