The logical status of diagrams:
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 a...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1994
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| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBY01 Volltext |
| Zusammenfassung: | 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 |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xi, 197 pages) |
| ISBN: | 9780511574696 |
| DOI: | 10.1017/CBO9780511574696 |
Internformat
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| 500 | |a Title from publisher's bibliographic system (viewed on 05 Oct 2015) | ||
| 520 | |a 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 | ||
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Datensatz im Suchindex
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| author | Shin, Sun-Joo |
| author_facet | Shin, Sun-Joo |
| author_role | aut |
| author_sort | Shin, Sun-Joo |
| author_variant | s j s sjs |
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| bvnumber | BV043945751 |
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| ctrlnum | (ZDB-20-CBO)CR9780511574696 (OCoLC)849997601 (DE-599)BVBBV043945751 |
| dewey-full | 511.3/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/3 |
| dewey-search | 511.3/3 |
| dewey-sort | 3511.3 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Philosophie |
| doi_str_mv | 10.1017/CBO9780511574696 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:24Z |
| institution | BVB |
| isbn | 9780511574696 |
| language | English |
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| physical | 1 online resource (xi, 197 pages) |
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| publishDate | 1994 |
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| spelling | Shin, Sun-Joo Verfasser aut The logical status of diagrams Sun-Joo Shin Cambridge Cambridge University Press 1994 1 online resource (xi, 197 pages) txt rdacontent c rdamedia cr rdacarrier Title from publisher's bibliographic system (viewed on 05 Oct 2015) 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 Venn diagrams Logic, Symbolic and mathematical Venn-Diagramm (DE-588)4835896-4 gnd rswk-swf Venn-Diagramm (DE-588)4835896-4 s 1\p DE-604 Erscheint auch als Druckausgabe 978-0-521-10277-3 Erscheint auch als Druckausgabe 978-0-521-46157-3 https://doi.org/10.1017/CBO9780511574696 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Shin, Sun-Joo The logical status of diagrams Venn diagrams Logic, Symbolic and mathematical Venn-Diagramm (DE-588)4835896-4 gnd |
| subject_GND | (DE-588)4835896-4 |
| title | The logical status of diagrams |
| title_auth | The logical status of diagrams |
| title_exact_search | The logical status of diagrams |
| title_full | The logical status of diagrams Sun-Joo Shin |
| title_fullStr | The logical status of diagrams Sun-Joo Shin |
| title_full_unstemmed | The logical status of diagrams Sun-Joo Shin |
| title_short | The logical status of diagrams |
| title_sort | the logical status of diagrams |
| topic | Venn diagrams Logic, Symbolic and mathematical Venn-Diagramm (DE-588)4835896-4 gnd |
| topic_facet | Venn diagrams Logic, Symbolic and mathematical Venn-Diagramm |
| url | https://doi.org/10.1017/CBO9780511574696 |
| work_keys_str_mv | AT shinsunjoo thelogicalstatusofdiagrams |