Synopses & Reviews
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
Challenges the prejudice against visualisation in logic and mathematics and provides a formal foundation for visual reasoning.
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 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.
Synopsis
This book examines the status of diagrams in logic. It presents Venn diagrams as a formal system of representation with rules of transformation that make this system sound and complete, thus demonstrating that valid proofs can be diagrammatic. The work counters a widespread and well known distrust of diagrams and it provides a formal foundation for work on natural reasoning in a visual mode.
Synopsis
This book examines the status of diagrams in logic. It presents Venn diagrams as a formal system of representation with rules of transformation that make this system sound and complete, thus demonstrating that valid proofs can be diagrammatic. The work counters a widespread and well known distrust of diagrams and it provides a formal foundation for work on natural reasoning in a visual mode.
Synopsis
This groundbreaking work will have important influence on research in logic, philosophy and knowledge representation.
Description
Includes bibliographical references (p. 193-194) and index.
Table of Contents
Acknowledgments; 1. Introduction; 2. Preliminaries; 3. Venn-I; 4. Venn-II; 5. Venn-II and Lo; 6. Diagrammatic versus linguistic representation; 7. Conclusion; Appendix; References; Index.