Table Of ContentDiagrammatic Representation and Reasoning
Springer-Verlag London Ltd.
Michael Anderson, Bernd Meyer
and Patrick Olivier (Eds)
Diagrammatic
Representation and
Reasoning
, Springer
Michael Anderson, MSc, PhD
Department of Computer and Information Sciences, Fordham University,
441 East Fordham Road, Bronx, NY 10458, USA
Bernd Meyer, Dr rer nat
School of Computer Science and Software Engineering, Monash University,
PO Box 26, Clayton Campus, Victoria 3800, Australia
Patrick Olivier, MA, MSc, PhD
Department of Computer Science, University of York, Hes1ington, York,
YOl05DD, UK
Cover images: Reproduced from Chapter 4 and used by kind permission ofProfessor Malcolm
Longair (eMalcolm Longair. AII rights reserved.)
British Library Cataloguing in Publication Data
Diagrammatic representation and reasoning
l.Artificial intelligence 2.Problem solving 3.Charts,
diagrams, etc.
I.Anderson, Michael II.Meyer, Bernd III.Olivier, Patrick
006.3
Library of Congress Cataloging-in-Publication Data
Diagrammatic representation and reasoning / Michael Anderson, Bemd Meyer, and
Patrick Olivier (eds.).
p.cm.
Includes bibliographical references and index.
ISBN 978-1-85233-242-6 (aIk. paper)
1. Automatic theorem proving. 2. Artificial intelligence. 3. Image processing. 4.
Problem solving. 1. Anderson, Michael, 1965-II. Meyer, Bemd, 1951-III. Olivier,
Patrick, 1966-
QA76.9.A96 D54 2000
006.3--dc21 00-063765
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ISBN 978-1-85233-242-6 ISBN 978-1-4471-0109-3 (eBook)
DOI 10.1007/978-1-4471-0109-3
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Preface
Diagrams are essential in most fields of human activity. There is substan
tial interest in diagrams and their use in many academic disciplines for the
potential benefits they may confer on a wide range of tasks. Are we now in
a position to claim that we have a science of diagrams-that is, a science
which takes the nature of diagrams and their use as the central phenom
ena of interest? If we have a science of diagrams it is certainly constituted
from multiple disciplines, including cognitive science, psychology, artificial
intelligence, logic, mathematics, and others.
If there is a science of diagrams, then like other sciences there is an appli
cations, or engineering, discipline that exists alongside the science. Applica
tions and engineering provide tests of the theories and principles discovered
by the science and extend the scope of the phenomena to be studied by gen
erating new uses of diagrams, new media for presenting diagrams, or novel
classes of diagram. This applications and engineering side of the science of di
agrams also comprises multiple disciplines, including education, architecture,
computer science, mathematics, human-computer interaction, knowledge ac
quisition, graphic design, engineering, history of science, statistics, medicine,
biology, and others.
The chapters of this book reflect this diversity of interests in the nature
and uses of diagrams and the synthesis of results presented at three recent
events on diagrammatic representation and reasoning: the American Associ
ation for Artificial Intelligence Fall Symposium on Diagrammatic Reasoning
held at MIT in November 1997; the Thinking with Diagrams Workshop held
at the University of Wales, Aberystywth, in August 1998, and the American
Association for Artificial Intelligence Fall Symposium on Formalizing Rea
soning with Visual and Diagrammatic Representations, held in Orlando in
October 1998. Without these events, this book would not have come about,
and therefore we would like to thank the American Association for Aritifi
cial Intelligence and the Engineering and Physical Sciences Research Council
(UK) for generous funding in supporting these meetings.
Michael Anderson April 2001
Bernd Meyer
Patrick Olivier
Contents
Part I. Views of Diagrams
1. Diagrams in the Mind? . . ... . .. ...... .... . . .. .. . . ... . . . . . . 7
2. Knowing About Diagrams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 29
3. A Meta-Taxonomy for Diagram Research ................. 47
4. Sketches as Mental Reifications of Theoretical
Scientific Treatment ...................................... 65
5. The Fundamental Design Variables of Diagramming ...... 85
Part II. Cognitive Aspects of Diagrams
6. Psychological Perspectives on Diagrams and their Users .. 109
7. Combining Semantic and Cognitive Accounts of
Diagrams ................................................. 125
8. Tactile Maps and a Test of the Conjoint Retention
Hypothesis ............................................... 141
9. Spatial Abilities in Problem Solving in Kinematics ....... 155
10. Graph Comprehension: The Role of Format, Content
and Individual Differences ................................ 173
11. Graphs in Print .......................................... 187
12. The Role of Representation and Working Memory in
Diagrammatic Reasoning and Decision Making ........... 207
13. Mechanical Reasoning about Gear-and-belt Diagrams:
Do Eye-movements Predict Performance? ................ 223
VIII Contents
14. How do Designers Shift their Focus of Attention in
their Own Sketches? ...................................... 241
Part III. Formal Aspects of Diagrammatic Reasoning
15. Diagrammatic Evaluation of Visual Mathematical
Notations ................................................. 261
16. A Topological Framework for Modelling Diagrammatic
Reasoning Tasks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
17. Multiple Readings of Peirce's Alpha Graphs .............. 297
18. On Automating Diagrammatic Proofs of Arithmetic
Arguments ............................................... 315
19. On the Practical Semantics of Mathematical Diagrams ... 339
20. EnE Sentences and Local Extent in Diagrams ............. 357
21. Implementing Euler/Venn Reasoning Systems ............ 371
22. Visual Spatial Query Languages: A Semantics Using
Description Logic ......................................... 387
Part IV. Applications of Diagrammatic Reasoning
23. Intelligent Diagrammatic Interfaces: State of the Art ..... 411
24. Towards Diagram Processing: A Diagrammatic
Information System ....................................... 431
25. Using Diagrams to Understand Diagrams:
A Case-Based Approach to Diagrammatic Reasoning .... 447
26. Interpreting the Engineer's Sketch: A Picture is
Worth a Thousand Constraints ........................... 467
27. Diagramming Research Designs ........................... 485
28. How to Build a (Quite General) Linguistic Diagram
Editor .................................................... 505
29. AVOW Diagrams: A Novel Representational System for
Understanding Electricity ................................ 521
Contents IX
30. AsbruView: Capturing Complex, Time-Oriented
Plans - Beyond Flow Charts .............................. 535
31. Acting with Diagrams: How to Plan Strategies in Two
Case Studies ............................................. 551
32. Specifying Diagram Languages by Means of
Hypergraph Grammars ................................... 565
Contributors
Herman J. Ader [email protected]
Vrije Universiteit, Clinical Epidemiology and Biostatistics, Van der Boe
chorststraat 7, 1081BT Amsterdam, The Netherlands.
Gerard Allwein [email protected]
Indiana University, Department of Computer Science, Lindley Hall 215,
Bloomington, IN 47405, USA.
Michael Anderson [email protected]
Fordham University, Department of Computer and Information Sciences,
441 East Fordham Road, Bronx, NY 10458, USA.
Daniela M. Bailer-Jones daniela. [email protected]
University of Bonn, Department of Philosophy, LFB I, Am Hof 1,53113 Bonn,
Germany.
Sidney C. Bailin [email protected]
Knowledge Evolution Inc., 1050 17th Street NW, Suite 520, Washington DC,
20036, USA.
Dave Barker-Plummer [email protected]
Stanford University, Center for the Study of Language and Information, Ven
tura Hall, Stanford, California, 94305-4115, USA.
Alan F. Blackwell [email protected]
University of Cambridge, Computer Laboratory, Cambridge, UK.
Mark Blades [email protected]
University of Sheffield, Psychology Department, Western Bank, Sheffield
S10 2TP, UK.
Alan Bundy [email protected]
University of Edinburgh, IRR, Division of Informatics, 80 South Bridge,
Edinburgh, EHI IHN, UK.
XII Contributors
Jo Calder [email protected]
University of Edinburgh, Division of Informatics, ICCS and LTG, Uni
versity of Edinburgh, Division of Informatics, 2 Buccleuch Place, Edin
burgh EH9 9LW, UK.
Peter C-H. Cheng [email protected]
University of Nottingham, ESRC Centre for Research in Development, In
struction and Thaining, School of Psychology, University Park, Nottingham
NG7 2RD, UK.
Nathalie Cousin-Rittemard [email protected]
Rennes 1 University, IRMAR, Equipe de Mecanique, Campus BEAULIEU,
Universite de Rennes 1, CS 74205 35042 Rennes Cedex, France.
Yuri Engelhardt [email protected]
University of Amsterdam, Department of Computational Linguistics, Palm
gracht 35,1015 HK Amsterdam, The Netherlands.
Dale E. Fish [email protected]
University of Connecticut, Department of Computer Science and Engineer
ing, School of Engineering, 261 Glenbrook Road, Storrs, CT 06269, USA.
Norman Foo [email protected]
University of New South Wales, Department of Computer Science and Engi
neering, Sydney NSW 2052, Australia.
Jean-Louis Giavitto [email protected]
CNRS, LaMI umr 8042, Universite d'Evry Val d'Essonne, Boulevard F. Mit
terrand, 91025 Evry Cedex, France.
Ian Green [email protected]
University of Edinburgh, IRR, Division of Informatics, 80 South Bridge,
Edinburgh, EHI IHN, UK.
Corin Gurr [email protected]
University of Edinburgh, Division of Informatics, 2 BuccIeuch Place, Edin
burgh EH8 9LW, UK.
Volker Haarslev [email protected]
University of Hamburg, Computer Science Department, Vogt-Kolln-Str. 30,
22527 Hamburg, Germany.
Mary Hegarty [email protected]
University of California, Santa Barbara, Psychology Department, Santa Bar
bara, CA 93106-9660, USA.
