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  • Book
  • © 2003

The Logic System of Concept Graphs with Negation

And Its Relationship to Predicate Logic

Authors:

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

Part of the book sub series: Lecture Notes in Artificial Intelligence (LNAI)

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Table of contents (14 chapters)

  1. Front Matter

  2. Start

    1. 1 Introduction

      • Frithjof Dau
      Pages 1-23
    2. 2 Basic Definitions

      • Frithjof Dau
      Pages 25-38
  3. Alpha

    1. 3 Overview for Alpha

      • Frithjof Dau
      Pages 39-40
    2. 6 Soundness and Completeness

      • Frithjof Dau
      Pages 63-80
  4. Beta

    1. 7 Overview for Beta

      • Frithjof Dau
      Pages 81-82
    2. 8 First Order Logic

      • Frithjof Dau
      Pages 83-91
    3. 9 Semantics for Existential Concept Graphs

      • Frithjof Dau
      Pages 93-105
    4. 10 Calculus for Existential Concept Graphs

      • Frithjof Dau
      Pages 107-123
    5. 11 Syntactical Equivalence to FOL

      • Frithjof Dau
      Pages 125-156
    6. 12 Summary of Beta

      • Frithjof Dau
      Pages 157-162
    7. 13 Concept Graphs without Cuts

      • Frithjof Dau
      Pages 163-185
  5. Appendix

    1. 14 Design Decisions

      • Frithjof Dau
      Pages 187-204
  6. Back Matter

About this book

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

  • School of Information Systems and Technology, University of Wollongong, Wollongong, Australia

    Frithjof Dau

Bibliographic Information

Buying options

eBook USD 39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions