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Logic and Visual Information

This book examines the logical foundations of visual information: information presented in the form of diagrams, graphs, charts, tables, and maps. The importance of visual information is clear from its frequent presence in everyday reasoning and communication, and also in computation. Chapters of the book develop the logics of familiar systems of diagrams such as Venn diagrams and Euler circles. Other chapters develop the logic of higraphs, Peirce diagrams, and a system having both diagrams and sentences among its well-formed representations. Syntax, semantics, rules of inference, and soundness and completeness results are provided for each of the systems. In addition to developing the logic of diagrams, key questions about the status of visual information are discussed, such as the relationship between language and visually-presented information.
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Table of Contents

Introduction; 1. Diagrams and Isomorphism; 1.1 Two-dimensionality; 1.2 Isomorphism thesis; 1.2.1 Informality; 1.2.2 Accidental isomorphism; 1.2.3 Literal preservation; 1.2.4 Non-literal preservation; 1.3 Conclusion; 2. Diagrams and Language; 2.1 Heterogeneous representations; 2.2 Text and meaning; 2.3 Text and efficiency; 2.4 Conclusion; 3. Diagrams and Rigor; 3.1 Proofs and diagrams; 3.2 Individuation of proofs; 3.3 Diagrams and formalization; 3.4 Conclusion; 4. Venn Diagrams; 4.1 Syntax; 4.2 Semantics; 4.3 Rules of inference; 4.4 Shin's theorem; 4.5 Completeness; 4.6 Definability; 4.7 Appendix: Proofs for chapter 4; 5. Venn Diagrams and First-Order Logic; 5.1 Syntax; 5.2 Semantics; 5.3 Rules of inference; 5.4 Completeness; 5.5 Appendix: diagrams and models; 6. Euler Circles; 6.1 Syntax; 6.2 Semantics; 6.3 Euler diagrams and Venn diagrams; 6.4 Rules of inference; 6.5 Completeness theorem; 7. Higraphs; 7.1 Syntax; 7.2 Semantics; 7.3 Rules of inference; 7.4 Completeness; 8. Peirce Diagrams; 8.1 Syntax; 8.1.1 Types and tokens; 8.1.2 Linear notation; 8.2 Semantics; 8.3 Rules of inference; 8.3.1 Provability and peircean provability; 8.4 Soundness; 8.5 Completeness; Conclusion; Bibliography; Indexes.


"This nice and clearly written book is an appropriate introduction to the contemporary subject of visual representation of logical systems." Branislav Boricic, Mathematical Reviews "Hammer is very clear and meticulous in presenting the technical material. His logicca analysis of diagrammatic systems will serve as future reference for anybody trying to formalize and legitimize the use of any particular kind of diagram." Isabel Luengo, Journal of symbolic Journal

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