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The Logic System of Concept Graphs with Negation

And Its Relationship to Predicate Logic

  • Frithjof Dau

Part of the Lecture Notes in Computer Science book series (LNCS, volume 2892)

Also part of the Lecture Notes in Artificial Intelligence book sub series (volume 2892)

Table of contents

  1. Front Matter
  2. Start

    1. Frithjof Dau
      Pages 1-23
    2. Frithjof Dau
      Pages 25-38
  3. Alpha

    1. Frithjof Dau
      Pages 39-40
    2. Frithjof Dau
      Pages 63-80
  4. Beta

    1. Frithjof Dau
      Pages 81-82
    2. Frithjof Dau
      Pages 83-91
    3. Frithjof Dau
      Pages 93-105
    4. Frithjof Dau
      Pages 107-123
    5. Frithjof Dau
      Pages 125-156
    6. Frithjof Dau
      Pages 157-162
    7. Frithjof Dau
      Pages 163-185
  5. Appendix

    1. Frithjof Dau
      Pages 187-204
  6. Back Matter

About this book

Introduction

The aim of contextual logic is to provide a formal theory of elementary logic, which is based on the doctrines of concepts, judgements, and conclusions. Concepts are mathematized using Formal Concept Analysis (FCA), while an approach to the formalization of judgements and conclusions is conceptual graphs, based on Peirce's existential graphs. Combining FCA and a mathematization of conceptual graphs yields so-called concept graphs, which offer a formal and diagrammatic theory of elementary logic.

Expressing negation in contextual logic is a difficult task. Based on the author's dissertation, this book shows how negation on the level of judgements can be implemented. To do so, cuts (syntactical devices used to express negation) are added to concept graphs. As we can express relations between objects, conjunction and negation in judgements, and existential quantification, the author demonstrates that concept graphs with cuts have the expressive power of first-order predicate logic. While doing so, the author distinguishes between syntax and semantics, and provides a sound and complete calculus for concept graphs with cuts. The author's treatment is mathematically thorough and consistent, and the book gives the necessary background on existential and conceptual graphs.

Keywords

Text calculus concept analysis concept graphs concept negation conceptual graphs contextual logics existential graphs formal concept analysis logic mathematical logic predicate logic relational graphs semantics syntax

Authors and affiliations

  • Frithjof Dau
    • 1
  1. 1.School of Information Systems and TechnologyUniversity of WollongongWollongongAustralia

Bibliographic information

  • DOI https://doi.org/10.1007/b94030
  • Copyright Information Springer-Verlag Berlin Heidelberg 2003
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-20607-1
  • Online ISBN 978-3-540-40062-2
  • Series Print ISSN 0302-9743
  • Series Online ISSN 1611-3349
  • Buy this book on publisher's site