Logical Reasoning with Diagrams
Published on 13. June 1996
287 pages
978-0-19-535586-4 (ISBN)
Description
One effect of information technology is the increasing need to present information visually. The trend raises intriguing questions. What is the logical status of reasoning that employs visualization? What are the cognitive advantages and pitfalls of this reasoning? What kinds of tools can be developed to aid in the use of visual representation? This newest volume on the Studies in Logic and Computation series addresses the logical aspects of the visualization of information. The authors of these specially commissioned papers explore the properties of diagrams, charts, and maps, and their use in problem solving and teaching basic reasoning skills. As computers make visual representations more commonplace, it is important for professionals, researchers and students in computer science, philosophy, and logic to develop an understanding of these tools; this book can clarify the relationship between visuals and information.
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Gerard Allwein | Jon Barwise
Logical Reasoning with Diagrams
Book
07/1996
Oxford University Press Inc
€291.50
Shipment within 15-20 days
Content
- Intro
- Contents
- Part A. Theoretical Issues
- Chapter I. Visual Information and Valid Reasoning
- 1 Introduction
- 2 The Legitimacy of Heterogeneous Inference
- 3 Hyperproof
- 4 Inference as Information Extraction
- 5 Conclusions
- Chapter II. Operational Constraints in Diagrammatic Reasoning
- 1 Introduction
- 2 Free Rides
- 3 Overdetermined Alternatives
- 4 A Formal Model
- 5 Conclusions
- Chapter III. Diagrams and the Concept of Logical System
- 1 The Standard Story
- 2 Examples of Diagrammatic Logics
- 3 Examples of Heterogeneous Logics
- 4 Classifications of Diagrammatic Systems
- 5 Conclusion
- Part B. Case Studies
- Chapter IV. Situation-Theoretic Account of Valid Reasoning with Venn Diagrams
- 1 Syntax
- 2 Semantics
- 3 Rules of Transformation
- 4 Soundness
- 5 Completeness
- Chapter V. Towards a Model Theory of Venn Diagrams
- 1 Syntax
- 2 Semantics
- 3 Rules of Inference
- 4 Soundness and Completeness
- Chapter VI. Peircean Graphs for Propositional Logic
- 1 Graphical Syntax
- 2 The Interpretation of Peircean Graphs
- 3 Rules of Inference
- 4 Soundness
- 5 Completeness
- Chapter VII. A Diagrammatic Subsystem of Hilbert's Geometry
- 1 Introduction
- 2 Syntax
- 3 Semantics
- 4 Rules of Transformation
- 5 Proofs
- 6 Soundness
- 7 Completeness
- Part C. Heterogeneous Systems
- Chapter VIII. Heterogeneous Logic
- 1 Historical Background
- 2 Logic and Information
- 3 Homomorphic Representations
- 4 Hyperproof
- 5 Towards a Mathematical Analysis of Hyperproof
- 6 Conclusions
- Chapter IX. Toward the Rigorous Use of Diagrams in Reasoning about Hardware
- 1 Introduction
- 2 The Circuitproof Project
- 3 Diagrams and Hardware Description
- 4 The Single-Pulser Example
- 5 A Mathematical Basis
- 6 Conclusions
- 7 Acknowledgments
- Chapter X. Exploiting the Potential of Diagrams in Guiding Hardware Reasoning
- 1 Introduction
- 2 Contrasting Diagrammatic and Sentential Representations
- 3 Heterogeneous Hardware Logic
- 4 The Island Traffic Light Controller
- 5 Conclusions
- 6 Acknowledgements
- Bibliography
- Index
- A
- B
- C
- D
- E
- F
- G
- H
- I
- J
- K
- L
- M
- N
- O
- P
- R
- S
- T
- U
- V
- W
- Z
