Qualitative Simulation Modeling and Analysis

355 Pages·1991·10.098 MB·English

by  Paul A. Fishwick (auth.), Paul A. Fishwick, Paul A. Luker (eds.)

Advances in Simulation
Volume 5
Series Editors:
Paul A. Luker
Bernd Schmidt
Advances in Simulation
Volume 1 Systems Analysis and Simulation I:
Theory and Foundations
Edited by A. Sydow, S.G. Tzafestas, and
R. Vichnevetsky
Volume 2 Systems Analysis and Simulation II:
Applications
Edited by A. Sydow, S.G. Tzafestas, and
T. Vichnevetsky
Volume 3 Advanced Simulation Biomedicine
Edited by Dietmar Moller
Volume 4 Knowledge-Based Simulation: Methodology
and Application
Edited by Paul A. Fishwick and
Richard B. Modjeski
Volume 5 Qualitative Simulation Modeling and
Analysis
Edited by Paul A. Fishwick and
Paul A. Luker
Paul A. Fishwick Paul A. Luker
Editors
Qualitative Simulation
Modeling and Analysis
With 121 Figures
Foreword by
Herbert A. Simon
Springer-Verlag
New York Berlin Heidelberg London
Paris Tokyo Hong Kong Barcelona
Editors:
Paul A. Fishwick Paul A. Luker
Computer and Information Department of Computer Science
Sciences Department California State University, Chico
University of Florida Chico, CA 95929-0410
Gainesville, FL 32611-2024 USA
USA
Series Editors:
Paul A. Luker Bernd Schmidt
Department of Computer Science Institut fUr Informatik
California State University, Chico Universitat Erlangen-Niirnberg
Chico, CA 95929-0410 Erlangen
USA FRG
Library of Congress Cataloging-in-Publication Data
Qualitative simulation modeling and analysis/Paul A. Fishwick. Paul
A. Luker, editors; foreword by Herbert A. Simon.
p. cm.-(Advances in simulation; v. 5)
Includes bibliographical references and index.
ISBN-13:978-0-387-97400-2
1. Computer simulation. I. Fishwick, Paul A. II. Luker, Paul A.
III. Series.
QA76.9.C65Q35 1991
oo3'.3-dc20 90-25822
Printed on acid-free paper.
© 1991 Springer-Verlag New York, Inc.
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ISBN -13: 978-0-387-97400-2 e-ISBN -13 :978-1-4613-9072-5
DOl: 10.1007/978-1-4613-9072-5
Foreword
The use of qualitative models of phenomena must go back to the beginnings
of human thought. If you overshoot the target, bring the bow a little lower
the next time. Of course, you must be careful to make moderate adjustments,
to keep the system homing on a stable equilibrium. This seems to us a very
natural way of thinking, and it hardly occurs to us to ask whether it can be
formalized or what are its limits.
With the advent of abstract mathematics, these questions arise in a new
form. Sometimes, we know the shape of the equations that govern the phe
nomena of interest, but we do not know the numerical values of parameters
perhaps, at most, we know their signs. Can we draw any conclusions about
the system behavior? Examples abound in economics and thermodynamics,
just to mention two domains. Experience tells us that, if the price of a
commodity is raised, the amount demanded will decrease, but the amount
offered by producers will increase. What will happen to the amount bought
and sold, and to the price, if a sales tax is imposed? Reason (qualitative reason)
tells us that less will be bought and sold than before, and that the price will
rise, but by less than the amount of the tax. What is the mechanism of the
reasoning that reaches these conclusions?
Or we look at the p-v diagram of a steam cycle, and notice that the volume
of the system increases at high pressure and then returns to its original value
at low pressure, so that the integral of pdv along the path is positive. We
conclude that work has been done around the cycle. What is the basis for our
conclusion?
Now it has been known for many years that such reasoning has a sound
mathematical foundation. In the economics example, for example, if we write
out the equations symbolically and shift the cost curve by the amount of the
tax, we can compute the new equilibrium values of price and quantity sym
bolically. Then, by taking account of the signs of certain partial derivatives
(the slopes of the supply and demand curves) and by assuming that the
equilibrium is stable (equivalent, again, to assumptions about the signs of
certain expressions); we can infer that the change in price will be positive, that
the change in quantity will be negative, and even that the change in price will
v
vi Foreword
be less than the tax. This computation is called by economists "the method of
comparative statics." Le Chatelier made use of essentially the same method
in his work on shifts in chemical equilibrium, leading to the famous "Le
Chatelier Principle."
Since the results depend only on the signs of certain quantities and since
these signs do not change if an arbitrary monotonic transformation is made
in the scales on which each of the variables is measured, it becomes clear that
these matters can be dealt with by the mathematics of monotonic transfor
mations, or, what is nearly the same thing, the mathematics of ordinally
measured quantities.
Surprisingly (at least it seems surprising to me), these matters do not receive
extensive treatment in the mathematical literature or in the curriculum in
elementary mathematics. Perhaps mathematicians find them too elementary
to be worthy of attention. At any rate, virtually every field of applied mathe
matics that stands to benefit from the use of qualitative reasoning has had to
reinvent these techniques for itself. As a result, their notations, their methods
of modeling, and their vocabularies form a cacophony of voices that com
municate poorly. Knowledge about qualitative reasoning that is won in one
discipline does not migrate rapidly and easily to others.
This volume brings together a number of these voices and their vocabu
laries, in order to allow them to be compared and understood. Most of them
are built upon the structure of ideas that I have suggested above-on notions
of the behavior of ordinally measured quantities-although the reader may
sometimes have to work a bit to make the connections.
But, as well as similarity, diversity deserves attention. We want to develop
qualitative reasoning as a working tool, which we can apply to various
domains and to problems with all kinds of structures. We can learn a great
deal from the examples in this book about the conditions under which par
ticular notations and computational schemes may be advantageous. Until the
mathematicians provide us with a suitable textbook on qualitative reasoning
with ordinal variables, perhaps we can use this volume as a textbook. And
even after the systematic textbook appears, we will want to see how the theory
applies to examples, of which quite a number are supplied here.
Formal treatments of qualitative reasoning and qualitative models of dy
namic systems are relatively new products. Even if it turns out that the
mathematics underlying them is relatively simple, new and interesting com
plexity will no doubt emerge when we apply them to real problem domains.
The techniques described in this book seem to me highly promising for
exploring the problem of complexity, and I would hope that its publication
will stimulate new research interest in this field, as well as new applications
of the techniques already developed.
Finally, as we think about qualitative reasoning, it is not too soon to explore
the new problems that arise when we try to apply our methods to domains
that are characterized by chaos (in the contemporary technical meaning of
that term). When we enter the world of nonlinear phenomena, and especially
Foreword vii
when we leave the domain where our systems tend toward stable equilibria
or stable limit cycles, what can we say about them? Even though we know
that detailed prediction of the future paths of chaotic systems is intrinsically
impossible, we need not give up trying to characterize their behavior qualita
tively. Already, we know, from the work of Mitchell Feigenbaum and others,
that bifurcation can be predicted on qualitative grounds, and that the shapes
of the strange attractors that replace equilibria in such systems can often be
inferred.
I do not suggest that the papers in this volume, which are directed at the
modeling of classical, nonchaotic systems, will provide answers to these ques
tions. I do suggest that an understanding of qualitative reasoning in this
"classical" domain may be a first step toward understanding how we can
reason qualitatively about chaos-about systems, for example, whose behavior
diverges with the slightest shift in initial conditions.
But the study of the healthy, robust organism must precede the study of
pathology. In this volume, you will find a substantial body of analysis of
systems that can be treated in terms of basic concepts of equilibrium, steady
state and disequilibrium, and of stability and instability. It provides plenty of
food for qualitative thought.
Pittsburgh, Pennsylvania Herbert A. Simon
Series Preface
To most people, simulation is, almost by definition, quantitative. At the heart
of many simulations are variables that take values in some continuous numer
ic range. The subject of this volume, qualitative modeling and simulation,
permits a view ofthe world that has, until recently, been ignored in simulation.
There are many situations in which it is not possible to quantify the attributes
in a way that has any meaning or validity. In other situations, although
quantification is possible, it is not appropriate for the particular study. The
"art" of simulation, if there is one, is to produce a model that is appropriate
for the task in hand. Qualitative modeling provides us with techniques that
enable the modeler to concentrate on what is known about the system being
modeled-our knowledge of this system is the key.
Qualitative modeling has developed from a number of roots. One of the
prominent ones is naive physics, in which relationships between real-world
objects are subjected to "commonsense" reasoning. Even more important,
perhaps, has been the influence of causal reasoning. Qualitative modeling
therefore has strong roots in artificial intelligence, for which the crucial com
ponent is the representation and manipulation of knowledge. The reader will
find this relationship quite evident, in a number of different ways, in the
chapters of this book. At the same time, it is interesting to note the breadth
of the collection as a whole.
I would like to thank the authors of the individual chapters in this book. A
special "thank you" goes to the coeditor of the volume, Paul A. Fishwick, who
took on greater than his fair share of the burden. I hope he reaps greater than
his fair share of the rewards.
I am very grateful to Gerhard Rossbach of Springer-Verlag for his endless
patience and for his faith in and commitment to the series.
As the complexity of our world increases, our dependence-that is not too
strong a word-on simulation also increases. Consequently, we are ever more
demanding of our simulations, or in other words, we are constantly seeking
Advances in Simulation. It was from a desire to document, share, and en
courage these advances that this series was created. We would like to cover
all aspects of advances in simulation, whether theoretical, methodological,
ix
x Series Preface
or hardware- or software-related. An important part of the publication of
material that constitutes an advance in some discipline is to make the material
available while it is still of considerable use. Gerhard and the production staff
at Springer-Verlag see to it that this is the case. I urge anybody who is eager
to share their advances in simulation to contact Bernd Schmidt or myself. We
would love to hear from you.
Chico, California Paul A. Luker
Preface
Qualitative simulation can be defined in a number of ways, from a variety of
perspectives. In general terms, it can be defined as a classification of simulation
and modeling methods that are primarily nonnumerical in nature. The
"qualitative" characterization of systems can apply itself to simulation in
put, output, model structure, and analysis method. Our study of qualitative
methodology does not preclude quantitative approaches; instead, we suggest
that qualitative approaches can augment traditional quantitative approaches
by making them more amenable to a wide range of simulation users with
differing levels of expertise, in both simulation methodology and the problem
domain. For instance, suppose that the knowledge available for a particular
simulation is not in numerical form; instead, it may be in linguistic form.
Somehow we must translate the natural language text into an intermediate
form acceptable by the simulation program. How do we accomplish this
translation effectively? This is just one instance where simulation input is not
in numerical form. Another instance relates to the kind of information ex
pressed in expert systems. Expert system knowledge is chiefly symbolic and
linguistic since human decision making is based largely on this type of in
formation. The study of how one can utilize symbolic forms in simulation
modeling is a key concern of qualitative simulation. Pictorial methods are
also very important in simulation modeling, since these methods allow users
to create system analogies by using graph-based techniques.
Studies in qualitative simulation are prompted by the following concerns:
1. Knowledge and data are sometimes symbolic or linguistic in form. How are
these forms integrated into simulation programs?
2. How are simulation models created over time? We term this process simula
tion model engineering and suggest that studies in qualitative methods can
enable us to take a step toward automating the simulation model construc
tion procedure.
3. We need to make the user interface between man and machine better.
Humans inherently think and reason in qualitative terms. Even though a
simulation model is quantitative, we need better man-machine interfaces,
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