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Acknowledgments | ||
1 | Introduction | 1 |
2 | Preliminaries | 11 |
2.1 | Euler diagrams | 12 |
2.2 | Venn diagrams | 16 |
2.3 | Venn-Peirce diagrams | 20 |
3 | Venn-I | 41 |
3.2 | Well-formed diagrams | 48 |
3.3 | Semantics | 62 |
3.4 | Equivalent diagrams and equivalent representing facts | 72 |
3.5 | Transformation | 80 |
3.6 | Soundness | 93 |
3.7 | Completeness | 98 |
4 | Venn-II | 111 |
4.2 | Well-formed diagrams | 115 |
4.3 | Semantics | 117 |
4.4 | Equivalent diagrams and equivalent representing facts | 119 |
4.5 | Transformation | 121 |
4.6 | Soundness | 125 |
4.7 | Completeness | 127 |
5 | Venn-II and L[subscript 0] | 141 |
5.1 | The language of L[subscript 0] | 141 |
5.2 | From set assignments to structures | 141 |
5.3 | From diagrams to sentences | 143 |
5.4 | From sentences to diagrams | 147 |
6 | Diagrammatic versus Linguistic Representation | 153 |
6.1 | Visuality and geometrical figures | 154 |
6.2 | Perceptual inferences | 157 |
6.3 | Venn-I as a diagrammatic system | 168 |
6.4 | Linguistic elements in Venn systems | 178 |
7 | Conclusion | 185 |
Appendix | 190 | |
References | 193 | |
Index | 195 |
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