Logic and Visual Information

by Hammer, Eric M.

• ISBN13: 9781881526872
• ISBN10: 1881526879
• Format: Hardcover
• Copyright: 1995-06-01
• Publisher: Stanford Univ Center for the Study
• More Book Details
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Summary

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.

Table of Contents

Introduction

Diagrams and Isomorphism

Two-dimensionality

Isomorphism thesis

Informality

Accidental isomorphism

Literal preservation

Non-literal preservation

Conclusion

Diagrams and Language

Heterogeneous representations

Text and meaning

Text and efficiency

Conclusion

Diagrams and Rigor

Proofs and diagrams

Individuation of proofs

Diagrams and formalization

Conclusion

Venn Diagrams

Syntax

Semantics

Rules of inference

Shin's theorem

Completeness

Definability

Appendix: Proofs for chapter 4

Venn Diagrams and First-Order Logic

Syntax

Semantics

Rules of inference

Completeness

Appendix: diagrams and models

Euler Circles

Syntax

Semantics

Euler diagrams and Venn diagrams

Rules of inference

Completeness theorem

Higraphs

Syntax

Semantics

Rules of inference

Completeness

Peirce Diagrams

Syntax

Types and tokens

Linear notation

Semantics

Rules of inference

Provability and peircean provability

Soundness

Completeness

Conclusion

Bibliography

Indexes

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