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Cover: 9780521102773 | The Logical Status of Diagrams | Shin Sun-Joo | Taschenbuch | Englisch
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The Logical Status of Diagrams
Taschenbuch von Sun-Joo Shin (u. a.)
Sprache: Englisch

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Beschreibung
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.
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.
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2008
Fachbereich: Grundlagen
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 212
ISBN-13: 9780521102773
ISBN-10: 0521102774
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Shin, Sun-Joo
Sun-Joo, Shin
Hersteller: Cambridge University Press
Maße: 229 x 152 x 13 mm
Von/Mit: Sun-Joo Shin (u. a.)
Erscheinungsdatum: 31.10.2008
Gewicht: 0,352 kg
preigu-id: 101674210
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2008
Fachbereich: Grundlagen
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 212
ISBN-13: 9780521102773
ISBN-10: 0521102774
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Shin, Sun-Joo
Sun-Joo, Shin
Hersteller: Cambridge University Press
Maße: 229 x 152 x 13 mm
Von/Mit: Sun-Joo Shin (u. a.)
Erscheinungsdatum: 31.10.2008
Gewicht: 0,352 kg
preigu-id: 101674210
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