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The Logical Status of Diagrams - Sun-Joo Shin

The Logical Status of Diagrams

(Autor)

Buch | Hardcover
212 Seiten
1995
Cambridge University Press (Verlag)
978-0-521-46157-3 (ISBN)
CHF 189,95 inkl. MwSt
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 27.1.1995
Zusatzinfo 148 Line drawings, unspecified
Verlagsort Cambridge
Sprache englisch
Maße 158 x 235 mm
Gewicht 467 g
Themenwelt Mathematik / Informatik Mathematik Logik / Mengenlehre
ISBN-10 0-521-46157-X / 052146157X
ISBN-13 978-0-521-46157-3 / 9780521461573
Zustand Neuware
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