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 this prejudice against visualization in the history of logic and mathematics 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.This pathbreaking book will have important influence on research in logic, philosophy, and knowledge representation.And in this century, it was Charles Peirce who made a great contribution to the further development of Venn diagrams. ... that my approach to Venn diagrams (in C~ and T)a#39; is the natural completion of these predecessorsa#39; incomplete projects.
|Title||:||The Logical Status of Diagrams|
|Publisher||:||Cambridge University Press - 1994|