The Logical Status of Diagrams

This groundbreaking work will have important influence on research in logic, philosophy and knowledge representation.

Sun-Joo Shin (Author)

9780521461573, Cambridge University Press

Hardback, published 27 January 1995

212 pages, 148 b/w illus.
23.5 x 15.8 x 1.5 cm, 0.467 kg

"Shin has shown that sysytems of diagrams can be developed that precisley parallel axiomatic formal systems for monadic predicate logic....Shin correctly points out what diagram systems and verbal systems can both do...that realistic pictures...can't." Phillip L. Peterson, Philosophy in Review

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.

Subject Areas: Mathematical logic [PBCD]