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The Logic System of Concept Graphs with Negation : And Its Relationship to Predicate Logic - Frithjof Dau

The Logic System of Concept Graphs with Negation

And Its Relationship to Predicate Logic

Paperback

Published: 24th November 2003
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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.

Introductionp. 1
Basic Definitionsp. 25
Overview for Alphap. 39
Semantics for Nonexistential Concept Graphsp. 41
Calculus for Nonexistential Concept Graphsp. 45
Soundness and Completenessp. 63
Overview for Betap. 81
First Order Logicp. 83
Semantics for Existential Concept Graphsp. 93
Calculus for Existential Concept Graphsp. 107
Syntactical Equivalence to FOLp. 125
Summary of Betap. 157
Concept Graphs without Cutsp. 163
Design Decisionsp. 187
Referencesp. 205
Indexp. 211
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540206071
ISBN-10: 3540206078
Series: Lecture Notes in Computer Science
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 216
Published: 24th November 2003
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.3 x 15.5  x 1.22
Weight (kg): 0.72