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Negations in Simple Concept Graphs

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Conceptual Structures: Logical, Linguistic, and Computational Issues (ICCS 2000)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1867))

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Abstract

The aim of this paper is to mathematically introduce negation to concept graphs (which are a mathematical modification of conceptual graphs) as a well-defined syntactical construct. First off, we discuss some questions which arise when negations for conceptual graphs are defined. In our view, a solution for these questions is to express negations by cuts in the sense of Peirce’s theory of existential graphs. A set-theoretical semantics for (nonexistential) concept graphs with cuts is developed in the framework of contextual logic. A modification of Peirce’s alpha-calculus, which is sound and complete, is presented.

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Author information

Authors and Affiliations

  1. Fachbereich Mathematik, Technische Universität Darmstadt, Schloßgartenstr. 7, D-64289, Darmstadt

    Frithjof Dau

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  1. Frithjof Dau
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Editors and Affiliations

  1. Institute of Algebra, University of Technology, Dresden, Germany

    Bernhard Ganter

  2. Département d’informatique et de génie logiciel, Université Laval, Pavillon Adrien-Pouliot, 1065, av. de la Médecine, G1V 0A6, Quebec City, Québec, Canada

    Guy W. Mineau

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Dau, F. (2000). Negations in Simple Concept Graphs. In: Ganter, B., Mineau, G.W. (eds) Conceptual Structures: Logical, Linguistic, and Computational Issues. ICCS 2000. Lecture Notes in Computer Science(), vol 1867. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10722280_18

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  • DOI: https://doi.org/10.1007/10722280_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67859-5

  • Online ISBN: 978-3-540-44663-7

  • eBook Packages: Springer Book Archive

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