Table Of ContentLecture Notes in Computer Science 1138
Edited by G. Goos, J. Hartmanis and J. van Leeuwen
Advisory Board: W. Brauer D. Gries J. Stoer
Jacques Calmet John A. Campbell
Jochen Pfalzgraf (Eds.)
Artificial Intelligence
dna Symbolic
lacitamehtaM noitatupmoC
International Conference, AISMC-3
Steyr, Austria, September 23-25, 6991
Proceedings
regnirpS
Series Editors
Gerhard Goos, Karlsruhe University, Germany
Juris Hartmani8, Cornell University, NY, USA
Jan van Leeuwen, Utrecht University, The Netherlands
Volume Editors
Jacques Calmet
University of Karlsruhe
Am Fasanengarten 5, D-76128 Karlsruhe, Germany
E-mail: [email protected]
John A. Campbell
University College London
Gower Street, WC1E 6BT London, United Kingdom
E-mail: [email protected]
Jochen Pfalzgraf
RISC-Linz, Johannes Kepler University
A-4040 Linz, Austria
E-mail: [email protected]
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Die Deutsche Bibliothek - CIP-Einheitsaufnahme
Artificial intelligence and symbolic mathematical computation :
international conference ; proceedings / AISMC-3, Steyr,
Austria, September 23 - 25, 1996. Jacques Calmet ... (ed.). -
Berlin ; Heidelberg ; New York ; Barcelona ; Budapest ; Hong
Kong ; London ; Milan ; Paris ; Santa Clara ; Singapore ;
Tokyo : Springer, 1996
(Lecture notes in computer science ; Vol. )8311
ISBN 3-540-61732-9
NE: Calmet, Jacques Hrsg.; AISMC <3, 1996, Steyr>; GT
CR Subject Classification (1991): 1.1-2, G.1-2,F.4.1
ISSN 0302-9743
ISBN 3-540-61732-9 Springer-Verlag Berlin Heidelberg New York
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Foreword
This volume of the Lecture Notes in Computer Science presents the proceed-
ings of the Third International Conference on Artificial Intelligence and Sym-
bolic Mathematical Computation (AISMC-3), held in Steyr (Austria), Septem-
ber 23-25, 1996, and organised by RISC-Linz (Research Institute for Symbolic
Computation, Universtiy of Linz) with support from ProFactor (Steyr).
The AISMC initiative is an interdisciplinary forum which aims at bringing to-
gether people from different areas of research and application fields. Emphasis is
on the interaction of methods and problem solving approaches from AI and sym-
bolic mathematical computations in a wide sense. The originators of the AISMC
initiative are Jacques Calmet and John A. Campbell. AISMC-3 continues the
successful events AISMC-1, organised by J.Calmet (Karlsruhe, August 1992),
and ASMC-2, organised by J.A.Campbell (Cambridge, August 1994). The pro-
ceedings of these conferences have been published as Springer LNCS volumes
737 and 958, respectively. It is intended to continue these meetings biannually.
An introductory overview of the basic ideas and intentions behind AISMC can
be found in the opening paper by the first two editors in the proceedings of
AIMSC-1.
To stress applications and to establish inks to engineering disciplines ew
incorporated in AISMC-3 the branch "Engineering and Industrial Applications".
At the end of the first conference day a panel discussion was devoted to this topic.
The conference site in Steyr is a restored old factory building which is now
a museum called "Museum industrielle Arbeitswelt". In this sense we consider
the conference as an event embedded in the local "cooperation triangle" Linz
Hagenberg - Steyr. This triangle was set up to integrate the cooperation of
-
university institutes and companies. Bruno Buchberger, the director and founder
of RISC, has been and still is one of the main propagators and initiators of this
idea.
The papers in the proceedings are listed according to the schedule of talks
at the conference. As one can see, the titles of the articles reflect the interdis-
ciplinary character of the meeting. Four invited talks are devoted to different
areas. We thank the invited speakers for timely sending the full manuscripts of
their contribution.
The conference is sponsored by AAAI, ProFactor (Steyr), RISC-Linz and
several other institutions and companies (which cannot be listed here as these
proceedings go to print). We are grateful to all of them. Last not least we would
like to thank all the program committee members and the referees for their
valuable support.
June 1996 seuqcaJ Calmet, John A. Campbell, Jochen Pfalzgraf
fV
Conference Committee: Jacques Calmet (Karlsruhe, Germany)
John A. Campbell (London, UK)
Jochen Pfalzgraf (Linz, Austria - Conference Chairman)
Program Committee: L. Aiello (Rome)
F. Arlabosse (Paris)
B. Buchberger (Linz)
G. Butler (Montreal)
R. Caferra (Grenoble)
J. Calmer (Karlsruhe)
J.A. Campbell (London)
.H Clausen (Salzburg)
A.M. Cohen (Eindhoven)
J. Cunningham (London)
H. Geiger (Munich)
R. Goebl (Vienna)
K. Hingerl (Steyr)
D. Kapur (Albany )YN
L. Kerschberg (Fairfax )AV
H. Kobayashi (Tokyo)
R. Leisen (Bonn)
A. Miola (Rome)
E. Orlowska (Warsaw)
J. Pfalzgraf (Linz)
F. Pfenning (Pittsburgh PA)
G. Reihart (Munich)
M. Rigg (Bracknell)
W, Roque (Porto Alegra)
J. Rosicky (Brno)
E. Sandewall (Linkbping)
K.U. Schulz (Munich)
A. Semenov (Novosibirsk)
T. Takeshima (Shizuoka)
T. Wilson (Ithaca )YN
Organized by: RISC-Linz, Johannes-Kepler-Universit~.t Linz
Local Organizers: M. Meisinger
M. Schleicher
V. Sofronie
K. Stokkermans
Table of Contents
Symbolic Computation and Teaching (Invited Lecture) ..................... 1
D.S. Scott
Analytica - An Experiment in Combining Theorem Proving and
Symbolic Computation ................................................... 12
A. Bauer, E. Clarke, X. Zhao
Document Recognition, Semantics, and Symbolic Reasoning in
Reverse Engineering of Software .......................................... 38
G. Butler, P. Grogono, R. Shinghal, I. Tjandra
Compromised Updates in Labelled Databases .............................. 49
F.C.C. Dargam
An Inference Engine for Propositional Two-valued Logic Based
no the Radical Membership Problem ...................................... 17
E. Roanes-Lozano, L.M. Laita, E. Roanes-Macfas
Programming yb Demonstration: A Machine Learning Approach
to Support Skill Acquisition for Robots "ILnevcittuerde ) .................. 87
R. Dillmann, H. Friedrich
Knowledge-Based Information Processing in Manufacturing Cells --
The Present and the Future ............................................. 901
G. Reinhart, R. Diesch, M.R. Koch
Calculi for Qualitative Spatial Reasoning (Invited Lecture) ............... 124
A.G. Cohn
Combining Local Consistency, Symbolic Rewriting and Interval
Methods ................................................................ 144
F. Benhamou, L. Granvilliers
Proof Transformation for Non-Compatible Rewriting ..................... 160
R. Biindgen
PATCH Graphs: An Efficient Data Structure for Completion of
Finitely Presented Groups ............................................... 176
C. Lynch, P. Strogova
Measuring the Likely Effectiveness of Strategies .......................... 191
B.J. Duple
viii
A New Approach on Solving 3-Satisfiability .............................. 197
R. Rodo~ek
Geometry Machines: From Artificial Intelligence to Symbolic
Mathematical Computation (Invited Lecture) ............................ 213
D. Wang
Interactive Theorem Proving and Finite Projective Planes ............... 240
J. Ueberberg
Towards Modelling the Topology of Homogeneous Manifolds
by means of Symbolic Computation ...................................... 258
M. Joswig
Solving Geometrical Constraint Systems Using CLP Based
on Linear Constraint Solver ............................................. 274
D. Bouhineau
Towards a Sheaf Semantics for Cooperating Agents Scenarios ............ 289
V. Sofronie
Data Types in Subdefinite Models ....................................... 305
V. Telerman, D. Ushakov
On Theorem-proving in Horn Theories with Built-in Algebras ............ 320
N. Andrianarivelo, W. Bousdira, J.-M. Talbot
Backward Reasoning in Systems with Cut ............................... 339
E. Eder
Soundness and Completeness versus Lifting Property .................... 354
J.A. Plaza
Reasoning with Preorders and Dynamic Sorts Using
Free Variable Tableaux .................................................. 365
A. Gavilanes, J. Leach, P.J. Martin, S. Nieva
Author Index ............................................................ 381
Symbolic Computation dna Teaching
Dana S. Scott
School of Computer Science
eigenraC Mellon ytisrevinU
Pittsburgh, Pennsylvania 15213, ASU
e-mail: [email protected]
Abstract. Since 1989, the author has tried to show that it is possible to put a complete
semester-long course in machine-held form. Several examples have been carried out (in
,)acitamehtaM and the paper reports on the experience, on the problems encountered, and
on some suggestions for future developments.
1 1. Twenty Questions
tn his keynote address at the Second Annual Conference on Technology in
Collegiate Mathematics in November 1989 at The Ohio State University (see
the newsletter UME TRENDS, for January 1990), Professor Lynn Steen effectively
spoke for parents and students, scientists and engineers, colleagues and administrators
by raising the following twenty snoitseuq for calculus .sremrofer Steen
suggested that responding to these questions could form an agenda for the current work
of people exploring the use of computers in curricular reform. Though several years
have passed since Steen wrote these words, the questions remain highly relevant, since
satisfactory conclusions about the use of computers have still not been reached.
In looking at the questions, remember they are addressed to mathematics
departments, not to computer science departments. Calculus reform is still today a
most controversial topic because so many students are required to take calculus, but
many mathematicians (in the United States) feel that "reform" has meant "dumbing-
down" to a level where the preparation of students in mathematics -- both at school
and college -- is being positively harmed. This is a very broad topic, however, and
we are only going to address here some of the problems about using computers and
symbolic computation in various other courses with mathematical content, and we
cannot enter here into the continuing battle over the future of the Calculus. All the
issues are connected, however.
Steen's questions can be broken into five sections:
Learning
1. Can computers help students understand mathematics?
2. Can students develop mathematical intuition without performing
extensive mathematical manipulations?
3. Do the mechanics of computing obscure mathematical insight?
4. Will using computers reduce students' facility to compute by hand?
Curriculum
$. How does computing change what students should know about
mathematics?
6. How does computing change what students can learn about
mathematics?
7. Where in the curriculum is computing most appropriate?
8. Will use of computers reduce the need for remediation?
Resourees
9. Can colleges afford computers for all mathematics students?
10. How much time and distraction is computing worth?
1 1. When will there be good software and compatible hardware?
12.Can textbooks ever reflect contemporary computer examples?
ar Teaching
13 .How much programming should be taught in mathematics courses?
14. Can pure mathematicians convey an appropriate computational
perspective?
1 $.How will new faculty fit into computer-enhanced programs?
16 .Will use of computers improve teaching of mathematics?
Dilemmas
17. Won't computer packages for calculus lead, as they have in statistics, to
much meaningless calculation?
18. If computers handle routine calculations, what will students do instead?
19. What are appropriate prerequisites for computer-based calculus courses?
2 0.Should mathematics be a lab science?
The author has many answers to and opinions on these questions. Providing
some answers and comments will form the main theme of this paper. The bottom
line is that, yes, I personally believe that mathematics should be in part a
laboratory science -- the problem in the past has been that we have not had sufficient-
ly powerful tools available to do the necessary experimentation on a large scale. Of
course, the computing machine does not replace imagination -- nor does the labo-
ratory in any other science. Neither does the machine replace the standard means of
exposition -- but it can make the composition and presentation of books and
lectures easier and more vivid, and more flexible. As with any tool, considerable
effort is required in learning to use it effectively. The financial investment for the
institution is considerable as well, The major question to ,eb discussed here is whether
the money and effort is worth the gain.
1 2. The Author's Experience
What follows is a brief chronological survey of the courses in which the author and
some of his associates have been involved. Then the syllabi of the projective
geometry and discrete mathematics course will be given later in this section
in some detail w especially to emphasize the point that it is possible to produce a
substantial semester-long course completely in a computer-based format.
Projective Geometry, Fall, '89, CMU Scott
Automata Theory, '90, '91, '93, Stevens Institute for Technology Sutner
Topics in Discrete Mathematics, Spr. '91, CMU Scott
Projective Geometry, Spr., '93, RISC-Linz Scott
Automata Theory, Spring '93, RISC-Linz Sutner
Introduction to ModMath, Spr. '94, CMU Scott, Miller
Introduction to ModMath, Fall '94, CMU Scott, Miller
Problem Solving, Spr. '95 CMU Scott, Miller, Sleator, Tygar
Introduction to ModMath, Spr. '95, CMU Miller, Statman
Introduction to ModMath, Fall '95, CMU Albert, Miller, Sumer
Introduction to ModMath, Spr. '96, CMU Scott, Miller, Sutner,
Walkington
As indicated, the first course attempted was a course in projective geometry
during the fall semester of 1989 at Carnegie Mellon (CMU). This was followed by a
"topics" course, where the students carried out various projects in discrete mathematics
and in using computer graphics. During a sabbatical year in Austria at RISC-Linz
('92/'93), the author gave another, improved version of the projective geometry
course. That same semester Klaus Sutner also gave at Linz a new version of his
course on finite automata, which he had developed over several years at the Stevens
Institute for Technology. These courses were presented in lectures with the instructor
using a projector from a computer, and sessions were held for students in a computer
cluster. We were very indebted to Professor Bruno Buchberger for the opportunity to
set up the computer classroom and to deliver these two courses. The very helpful staff
and students at RISC-Linz we also essential for making things work.
After returning to the States, Scott began development of an introductory
course in discrete mathematics for first-year students with the assistance of Philip L.
Miller, head of the Introductory Programming Group at CMU. The computer-based
classrooms used for programming were employed for the laboratory sessions, and
lectures were given in classrooms with a projector. A more advanced course in
discrete mathematics was also tried out with the cooperation of other CS faculty.
Sutner then joined the teaching faculty in the Introductory Programming Group in
Computer Science at CMU in the fall of 1995. The introductory course had also
been rerun twice and a complete revision was made for the Spring Semester 1996,
with-the cooperation of Miller and Sutner and other CMU faculty.
Some acknowledgments are in order. Over the years, Scott has been very ably
assisted at various times by four of his former students: Jean-Philippe Vidal (Paris),
Marko Petkovsek (Ljubljana, Slovenia), and J. Todd. Wilson (Cornell), Drew Dean
(Princeton), and by one post-doctoral visitor, Dr. Christine Luksch (Darmstadt). He is
much indebted to them. Essential advice about Mathematica and about computer-
based teaching has been obtained at various times from Prof. John Gray (Illinois) and
from many people at Wolfram Research, Inc. (Urbana, Illinois), including Stephen
Wolfram, Theo Gray, Roman Maeder, Igor Rivin, Henry Cejtin, Cameron Smith, and
Nancy Blachman. However, without the extensive involvement, both in planning and
in execution, by Philip Miller and Klaus Sutner, the later courses could never have
been concieved, mounted or completed. The two of them have been wonderful collab-
orators and friends, and we hope to continue joint work with new teaching develop-
merits in the future.
