The Logical Status of Diagrams
By (author) Sun-Joo Shin
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Logical Status of Diagrams by Sun-Joo Shin
Book DescriptionDiagrams are widely used in reasoning about problems in physics, mathematics and logic, but have traditionally been considered to be only heuristic tools and not valid elements of mathematical proofs. This book challenges this prejudice against visualisation in the history of logic and mathematics and provides a formal foundation for work on natural reasoning in a visual mode. The author presents Venn diagrams as a formal system of representation equipped with its own syntax and semantics and specifies rules of transformation that make this system sound and complete. The system is then extended to the equivalent of a first-order monadic language. The soundness of these diagrammatic systems refutes the contention that graphical representation is misleading in reasoning. The validity of the transformation rules ensures that the correct application of the rules will not lead to fallacies. The book concludes with a discussion of some fundamental differences between graphical systems and linguistic systems. This groundbreaking work will have important influence on research in logic, philosophy and knowledge representation.
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Book DetailsISBN: 9780521461573
(228mm x 152mm x 16mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 27-Jan-1995
Country of Publication: United Kingdom
Books By Author Sun-Joo Shin
Logical Status of Diagrams, Paperback (March 2009)
This groundbreaking work will have important influence on research in logic, philosophy and knowledge representation.
Iconic Logic of Peirces Graphs, Hardback (June 2002)» View all books by Sun-Joo Shin
A case study of multimodal systems and a new interpretation of Charles S. Peirce's theory of reasoning and signs based on an analysis of his system of Existential Graphs.
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