The logical status of diagrams:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge u.a.
Cambridge Univ. Press
1994
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 197 S. Ill., graph. Darst. |
| ISBN: | 052146157X |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV010351243 | ||
| 003 | DE-604 | ||
| 005 | 19980805 | ||
| 007 | t | ||
| 008 | 950823s1994 ad|| |||| 00||| eng d | ||
| 020 | |a 052146157X |9 0-521-46157-X | ||
| 035 | |a (OCoLC)30079193 | ||
| 035 | |a (DE-599)BVBBV010351243 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-739 |a DE-29 |a DE-91G |a DE-11 | ||
| 050 | 0 | |a QA248 | |
| 082 | 0 | |a 511.3/3 |2 20 | |
| 084 | |a CC 2500 |0 (DE-625)17609: |2 rvk | ||
| 084 | |a CC 2600 |0 (DE-625)17610: |2 rvk | ||
| 084 | |a SK 130 |0 (DE-625)143216: |2 rvk | ||
| 084 | |a DAT 540f |2 stub | ||
| 084 | |a MAT 039f |2 stub | ||
| 100 | 1 | |a Shin, Sun-Joo |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The logical status of diagrams |c Sun-Joo Shin |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge u.a. |b Cambridge Univ. Press |c 1994 | |
| 300 | |a XI, 197 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Logic, Symbolic and mathematical | |
| 650 | 4 | |a Venn diagrams | |
| 650 | 0 | 7 | |a Venn-Diagramm |0 (DE-588)4835896-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Venn-Diagramm |0 (DE-588)4835896-4 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006890666&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-006890666 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Record in the Search Index
| _version_ | 1804124774613385216 |
|---|---|
| adam_text | Contents
Acknowledgments page xi
1 Introduction 1
2 Preliminaries 11
2.1 Euler diagrams 12
2.2 Venn diagrams 16
2.3 Venn Peirce diagrams 20
2.3.1 Modification of Venn diagrams 21
2.3.2 Rules of transformation 24
3 Venn I 41
3.1 Preliminary remarks 43
3.2 Well formed diagrams 48
3.2.1 Primitive objects 48
3.2.2 Talking about the objects: pseudonaming 49
3.2.3 Counterpart relations 53
3.2.4 Well formed diagrams 57
3.3 Semantics 62
3.3.1 Set assignments 64
3.3.2 Representing facts 68
3.3.3 Consequence relation 71
3.4 Equivalent diagrams and equivalent representing facts 72
3.4.1 Equivalent diagrams 73
3.4.2 Equivalent representing facts 77
3.5 Transformation 80
3.5.1 Rules of transformation 81
3.5.2 Formal obtainability 92
vii
viii Contents
3.6 Soundness 93
3.6.1 Validity of rules of transformation 93
3.6.2 Soundness theorem 97
3.7 Completeness 98
3.7.1 Maximal diagram 98
3.7.2 Completeness theorem 109
4 Venn II 111
4.1 Preliminary remarks 113
4.2 Well formed diagrams 115
4.2.1 Primitive objects 115
4.2.2 Well formed diagrams 116
4.2.3 Counterpart relations 117
4.3 Semantics 117
4.4 Equivalent diagrams and equivalent representing facts 119
4.4.1 Equivalent diagrams 119
4.4.2 Equivalent representing facts 120
4.5 Transformation 121
4.5.1 Rules of transformation 121
4.5.2 Formal obtainability 125
4.6 Soundness 125
4.6.1 Validity of transformation rules 125
4.6.2 Soundness theorem 127
4.7 Completeness 127
4.7.1 Maximal diagram 127
4.7.2 Elaborated maximal diagram 129
4.7.3 Completeness theorem 132
5 Venn II and Xo I41
5.1 The language of jS?o 141
5.2 From set assignments to structures 141
5.3 From diagrams to sentences 143
5.3.1 From regions to formulas 144
5.3.2 From representing facts to sentences 145
5.3.3 From diagrams to sentences 146
5.4 From sentences to diagrams 147
5.4.1 From formulas to regions 149
5.4.2 From sentences to diagrams 149
Contents ix
6 Diagrammatic versus Linguistic Representation 153
6.1 Visuality and geometrical figures 154
6.2 Perceptual inferences 157
6.2.1 Relations among objects 160
6.2.2 Conjunctive information 163
6.2.3 Tautologies and contradictions 166
6.3 Venn I as a diagrammatic system 168
6.3.1 Relations of sets 168
6.3.2 Conjunctive information 173
6.3.3 Tautologies and contradictions 176
6.4 Linguistic elements in Venn systems 178
6.4.1 Disjunctive information 180
6.4.2 Primary versus secondary show 181
7 Conclusion 185
Appendix 190
References 193
Index 195
|
| any_adam_object | 1 |
| author | Shin, Sun-Joo |
| author_facet | Shin, Sun-Joo |
| author_role | aut |
| author_sort | Shin, Sun-Joo |
| author_variant | s j s sjs |
| building | Verbundindex |
| bvnumber | BV010351243 |
| callnumber-first | Q - Science |
| callnumber-label | QA248 |
| callnumber-raw | QA248 |
| callnumber-search | QA248 |
| callnumber-sort | QA 3248 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | CC 2500 CC 2600 SK 130 |
| classification_tum | DAT 540f MAT 039f |
| ctrlnum | (OCoLC)30079193 (DE-599)BVBBV010351243 |
| 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 | Informatik Mathematik Philosophie |
| edition | 1. publ. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01623nam a2200457 c 4500</leader><controlfield tag="001">BV010351243</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">19980805 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">950823s1994 ad|| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">052146157X</subfield><subfield code="9">0-521-46157-X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)30079193</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV010351243</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-739</subfield><subfield code="a">DE-29</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA248</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">511.3/3</subfield><subfield code="2">20</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">CC 2500</subfield><subfield code="0">(DE-625)17609:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">CC 2600</subfield><subfield code="0">(DE-625)17610:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 130</subfield><subfield code="0">(DE-625)143216:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">DAT 540f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 039f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Shin, Sun-Joo</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">The logical status of diagrams</subfield><subfield code="c">Sun-Joo Shin</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">1. publ.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge u.a.</subfield><subfield code="b">Cambridge Univ. Press</subfield><subfield code="c">1994</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XI, 197 S.</subfield><subfield code="b">Ill., graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Logic, Symbolic and mathematical</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Venn diagrams</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Venn-Diagramm</subfield><subfield code="0">(DE-588)4835896-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Venn-Diagramm</subfield><subfield code="0">(DE-588)4835896-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006890666&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-006890666</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV010351243 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:51:01Z |
| institution | BVB |
| isbn | 052146157X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006890666 |
| oclc_num | 30079193 |
| open_access_boolean | |
| owner | DE-739 DE-29 DE-91G DE-BY-TUM DE-11 |
| owner_facet | DE-739 DE-29 DE-91G DE-BY-TUM DE-11 |
| physical | XI, 197 S. Ill., graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Shin, Sun-Joo Verfasser aut The logical status of diagrams Sun-Joo Shin 1. publ. Cambridge u.a. Cambridge Univ. Press 1994 XI, 197 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics Mathematik Logic, Symbolic and mathematical Venn diagrams Venn-Diagramm (DE-588)4835896-4 gnd rswk-swf Venn-Diagramm (DE-588)4835896-4 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006890666&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Shin, Sun-Joo The logical status of diagrams Mathematics Mathematik Logic, Symbolic and mathematical Venn diagrams 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 | Mathematics Mathematik Logic, Symbolic and mathematical Venn diagrams Venn-Diagramm (DE-588)4835896-4 gnd |
| topic_facet | Mathematics Mathematik Logic, Symbolic and mathematical Venn diagrams Venn-Diagramm |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006890666&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT shinsunjoo thelogicalstatusofdiagrams |