The Logical Status of Diagrams

The Logical Status of Diagrams

By: Sun-Joo Shin (author)Paperback

Special OrderSpecial Order item not currently available. We'll try and order for you.

Description

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.

Contents

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.

Product Details

  • ISBN13: 9780521102773
  • Format: Paperback
  • Number Of Pages: 212
  • ID: 9780521102773
  • weight: 320
  • ISBN10: 0521102774

Delivery Information

  • Saver Delivery: Yes
  • 1st Class Delivery: Yes
  • Courier Delivery: Yes
  • Store Delivery: Yes

Prices are for internet purchases only. Prices and availability in WHSmith Stores may vary significantly

Close