Overview
- Includes supplementary material: sn.pub/extras
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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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.
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Table of contents (14 chapters)
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Front Matter
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Appendix
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Back Matter
Authors and Affiliations
Bibliographic Information
Book Title: The Logic System of Concept Graphs with Negation
Book Subtitle: And Its Relationship to Predicate Logic
Authors: Frithjof Dau
Series Title: Lecture Notes in Computer Science
DOI: https://doi.org/10.1007/b94030
Publisher: Springer Berlin, Heidelberg
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 2003
Softcover ISBN: 978-3-540-20607-1Published: 24 November 2003
eBook ISBN: 978-3-540-40062-2Published: 15 December 2003
Series ISSN: 0302-9743
Series E-ISSN: 1611-3349
Edition Number: 1
Number of Pages: XII, 216
Topics: Mathematical Logic and Foundations, Artificial Intelligence, Computer Science, general, Mathematical Logic and Formal Languages, Discrete Mathematics in Computer Science