The Logical Status of Diagrams

Sun-Joo Shin (Autor)

Buch | Softcover

212 Seiten

2009
Cambridge University Press (Verlag)
978-0-521-10277-3 (ISBN)

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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 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.

Acknowledgements; 1. Introduction; 2. Preliminaries; 3. Venn-I; 4. Venn-II; 5. Venn-II and L0; 6. Diagrammatic versus linguistic representation; 7. Conclusion; Appendix; References; Index.

Erscheint lt. Verlag	12.3.2009
Zusatzinfo	148 Line drawings, unspecified
Verlagsort	Cambridge
Sprache	englisch
Maße	152 x 229 mm
Gewicht	320 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
ISBN-10	0-521-10277-4 / 0521102774
ISBN-13	978-0-521-10277-3 / 9780521102773
Zustand	Neuware