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International Conference on Conceptual Structures

ICCS 2001: Conceptual Structures: Broadening the Base pp 72–86Cite as

Concept Graphs and Predicate Logic

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2120))

Abstract

In the ICCS 2000 proceedings we introduced negation to simple concept graphs without generic markers by adding cuts to their definition. The aim of this paper is to extend this approach of cuts to simple concept graphs with generic markers. For these graphs, a set-theoretical semantics is presented. After this a modification of Peirce’s beta-calculus is provided, and definitions for mappings Φ and Ψ between concept graps and first order logic are given. If we consider both concept graphs and first order logic formulas, together with their particular derivability relations, as quasiorders, Φ and Ψ are mutually inverse quasiorder isomorphisms between them. The meaning of this fact is elaborated. Finally we provide a result that links the semantics of concept graphs and the semantics of first order logic. This result can be used to show that the calculus for concept graphs is sound and complete.

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References

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Author information

Authors and Affiliations

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

    Frithjof Dau

Authors
  1. Frithjof Dau
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Editor information

Editors and Affiliations

  1. Computer Science Department, TH N-351, University of Alabama in Huntsville, Huntsville, AL, 35899, USA

    Harry S. Delugach

  2. Institut für Angewandte Informatik und Formale Beschreibungsverfahren (AIFB), Universität Karlsruhe (TH), 76128, Karlsruhe, Germany

    Gerd Stumme

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© 2001 Springer-Verlag Berlin Heidelberg

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Dau, F. (2001). Concept Graphs and Predicate Logic. In: Delugach, H.S., Stumme, G. (eds) Conceptual Structures: Broadening the Base. ICCS 2001. Lecture Notes in Computer Science(), vol 2120. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44583-8_6

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  • DOI: https://doi.org/10.1007/3-540-44583-8_6

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42344-7

  • Online ISBN: 978-3-540-44583-8

  • eBook Packages: Springer Book Archive

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