The Logical Status of Diagrams - Softcover

Shin, Sun-Joo

 
9780521102773: The Logical Status of Diagrams
Softcover
ISBN 10: 0521102774 ISBN 13: 9780521102773
Publisher: Cambridge University Press, 2009

Synopsis

Diagrams 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 proof. This book challenges the prejudice against visualization 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 and specifies rules of transformation that make this system sound and complete. The soundness of the diagrammatic system refutes the contention that graphical representation is misleading in reasoning. The book concludes with a discussion of some fundamental differences between graphical systems and linguistic systems.

"synopsis" may belong to another edition of this title.

From the Back Cover

Diagrams 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 visualization 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.

"About this title" may belong to another edition of this title.

Publisher
Cambridge University Press
Publication date
2009
Language
English
ISBN 10 
0521102774
ISBN 13 
9780521102773
Binding
Paperback
Edition number
1
Number of pages
212

Other Popular Editions of the Same Title

9780521461573: The Logical Status of Diagrams

Featured Edition

ISBN 10:  052146157X ISBN 13:  9780521461573
Publisher: Cambridge University Press, 1995
Hardcover