IEEE TRANSACTIONS ON SYSTEMS, MAN AND CYBERNETICS, VOL. XX, NO. Y, MONTH 1993
A Multimodel Approach to Reasoning and
Simulation
Paul A. Fishwick N. Hari Narayanan Jon Sticklen Andrea Bonarini
Abstract Models that are constructed within the bounds
of a single paradigm are not sufficient for modeling all as
pects of complex systems. Therefore, even though reason
ing and simulation systems that utilize a single modeling
paradigm are the current norm, we explore a multimodel ap
proach in this paper. A multimodel approach is defined as
one in which more than one model each derived from
a different perspective, and utilizing correspondingly dis
tinct reasoning and simulation strategies are employed.
By describing four models which illustrate the use of dif
ferent modeling techniques, we show how a multimodel ap
proach can enrich the modeling environment and make it
correspond better with real world information. Our mod
els come from many sources Systems and Simulation Theory
for the modeling of natural phenomena and artificial devices,
and Artificial I and Cognitive Science for the modeling
of human intuition and expertise in reasoning. Generaliz
ing from these four models, we suggest that modeling com
plex systems may best be approached from an integrated
architectural viewpoint which combines multiple modeling
paradigms.
Keywords Multimodeling,VisuoSpatial Reason
ing,Abstraction Levels,Qualitative System,Functional Mod
eling.
I. INTRODUCTION
T HE advent of computers provided a powerful tool for
deriving the behavior of complex systems: simulation.
The corresponding research discipline, Systems and Sim
ulation Theory, has grown to provide theoretical founda
tions and practical tools for computerbased simulation.
However, systems that are thus studied have become in
creasingly complex. These now include systems with com
ponents for which complete analytical models may not be
available (i.e., ecological systems) and systems with in
telligent agents as components (i.e., social systems). For
such systems, the traditional approach to simulation, in
which a user programs a single simulation model with ini
tial (boundary) conditions, runs the simulation program,
and interprets the typically voluminous data that the pro
gram outputs, is proving to be inadequate. There is a need
for incorporating ,,i. II, ...." into simulation programs
to provide the user with support in setting up simulation
models, to have the simulation guided intelligently at run
Paul A. Fishwick is Associate Professor with the Dept. of Com
puter and Information Sciences, University of Florida. Email: fish
wick@cis.ufl.edu .
N. Hari Narayanan is a Visiting Research Scientist at the
Advanced Research Laboratory of Hitachi, Ltd. Email:
Jon Sticklen is Associate Professor with the Dept. of
Computer Science Michigan State University. Email:
sticklen@cpswh.cps.msu.edu .
Andrea Bonarini is Assistant Professor with the Dept. of Electron
ics Engineering at the Politecnico di Milano, Italy. Email: bonar
ini@ipmel2.elet.polimi.it .
time, and to provide support for interpreting the simu
lation results. This need is being met by reasoning tools
and techniques from Simulation, Artificial Intelligence, and
models of human cognition from Cognitive Science. Recent
AI and Simulation Workshops that have been held in con
junction with the National Conferences on Artificial Intel
ligence (AAAI) and a conference series entitled AI, Simu
lation and Planning in High Autonomy Systems [1] provide
ample testimony to increasing interest in this confluence of
disciplines.
A fortuitous result of these developments has been the
realization that reasoning (as investigated in AI and Cog
nitive Science) and simulation (as investigated in Systems
and Simulation Theory) have much to contribute to each
other. In simulation literature we see many papers dis
cussing how reasoning techniques have been profitably in
corporated into traditional simulation models [2], [3], [4],
[5], [6], [7], [8], while in AI literature we see the growth
of a subarea called Qualitative Reasoning about Physical
Systems [9] that uses "qualitative simulation" [10] as a
technique for deriving, and subsequently reasoning about,
system behaviors. We now offer some initial observations
based on the synthesis of AI and simulation research.
A capability for intelligently reasoning about the evo
lution of a simulation is of benefit to simulation mod
els.
A capability for simulating the behavior of systems is
of advantage to reasoning programs.
It follows that integrated systems capable of both sim
ulation and reasoning will provide leverage in dealing
with a wide variety of complex systems.
Given this context, our central thesis is that a multimodel
approach is an appropriate way to exploit the advantages
of simulation models and reasoning techniques within a sin
gle system. We define a multimodel approach as one with
a knowledge representation scheme composed of different
types of knowledge coupled together. Each type of knowl
edge may provide the basis for a reasoning capability to be
used for one aspect of the problem that the overall system
addresses. For example, a bond graph is useful for mod
eling and simulating the energy flow characteristics of a
physical system, but a functional model1 may be more ap
propriate for reasoning about how the system components
contribute to its overall functioning.
Any real world system can be understood at varying lev
els of abstraction. As one progressively moves to a more
detailed view of the system, eventually, the complexity one
1We use the word "functional" in this instance to refer to the func
tionality (or "purpose") of the device, and not the lowlevel transfer
functions that may be a part of a mathematical model.
IEEE TRANSACTIONS ON SYSTEMS, MAN AND CYBERNETICS, VOL. XX, NO. Y, MONTH 1993
encounters is overwhelming. Although all real systems have
this property, some systems present great complexity even
at the most abstract level of understanding systems
such as ecological systems or engineered chemical refining
plants. To reason about such complex organization, a prob
lem solver might rely on more than one type of knowledge
organization.
For example, ecologists pondering the causeeffect rela
tions that might lead to global warming phenomena might
first use "rule of thumb" heuristic knowledge organizations
to obtain clues for what part of a large causal knowledge
base might hold useful information. Then they might go
on to explore (qualitatively) a causalnet like structure that
could lead to a conjecture on what might happen should
production of carbon dioxide increase by a factor of two.
Finally, they might use this qualitative suggestion to ini
tiate a large numerical simulation of the conjectured situ
ation. Such a progression from compiledlevel knowledge
organizations, to modelbased structures, to numerical cal
culations, is necessary since no single modeling method will
serve to answer all questions about the system's behavior.
However, most traditional AI systems and simulation
models involve a single paradigm or knowledge organiza
tion. For instance, an AI system may be based on seman
tic networks, fuzzy logic, or production rules; a simulation
model may be based on a Markov model, differential equa
tions, or a Petri net. We argue that a knowledge organi
zation scheme composed of a variety of models, with each
providing a reasoning or simulation capability for address
ing one aspect of the problem, is the most effective way of
tackling a complex problem at varying levels of abstraction.
II. OVERVIEW
While a multimodel approach can provide different per
spectives on a problem and facilitate addressing the prob
lem from different levels of abstraction, one should also be
concerned with properly integrating different models (or
types of knowledge organization). In this paper however,
we have chosen to focus on the models themselves, and we
concentrate on the following four areas:
VisuoSpatial Reasoning: If we have information in the
form of a diagram depicting the spatial configuration
of the components of a device, along with some basic
knowledge regarding the components, can we derive
the spatial behaviors of the device by a combination of
predictive reasoning and visualizations (image trans
formations)?
Functional Modeling: Suppose that we know the pur
poses (or goals) of a device and its component subde
vices. Can the organization of our causal understand
ing of the device be used as a framework for integrating
numerical relationships which govern the detailed be
havior of the device? Moreover, can this integration of
causally indexed, qualitative understanding with nu
merical relationships be used as a basis for numerical
simulation?
Qualitative and Numerical Data in Simulation: We
may find that we have a welldefined, numerical model
of a part of a complex system, and only incomplete,
qualitative knowledge about another part of it. How
can we simulate and reason about such systems?
Multimodel Integration: With a multimodel scenario,
the modeling task is complicated by the requirement
of maintaining consistency across levels of abstraction.
How can we design multilevel models so that models
at one level serve as valid abstractions of models at
lower levels?
A model for visuospatial reasoning, one which facilitates
reasoning about spatial behaviors of device components
from schematic diagrams, is described by Narayanan in
Section 3. A mathematical model does not contain any ex
plicit knowledge of the goal or purpose of the modeled sys
tem. In Section 4 Sticklen shows how the functional model
ing technique addresses this drawback by organizing causal
knowledge about a system around its known teleology and
by incorporating mathematical relationships among state
variables within this knowledge structure. Bonarini recog
nizes that integrating qualitative and numerical simulation
models can mitigate limitations of each type of simulation
while retaining their advantages. In Section V he describes
such an integrated model. Fishwick describes the method
of multimodel integration in Section VI. In the concluding
section (Section VII) we will discuss how these four dif
ferent models contribute to a multimodel approach toward
reasoning and simulation. Their differences serve to enrich
such a multimodel system in comparison with one that de
pends on a single modeling paradigm. Thus, we propose
that the use of multiple types of knowledge in modeling
complex real world systems has a tremendous advantage
over the use of a reasoning system which is monolithic in
nature.
The seeds of this collaboration among the four authors
(whose backgrounds span Systems and Simulation Theory,
AI, and Cognitive Science) were sown at the Al, Simula
tion and Planning in High Autonomy Systems conference
held in April 1991 at Cocoa Beach, Florida [1]. There it be
came clear that both reasoning and simulation approaches
were going to be necessary for addressing the challenges
that complex systems pose. This motivated the prepara
tion of a collaborative paper on multimodel reasoning and
simulation.2
III. VISuoSPATIAL REASONING: A VISUAL APPROACH
TO COMMONSENSE SPATIAL REASONING (VSRM)
A capability to reason about how devices operate is
clearly an important one for reasoning and simulation sys
tems. Many devices contain mechanisms with spatial be
haviors. Not surprisingly, the problem of reasoning about
spatial behaviors of mechanisms has received much atten
tion in AI [11], [12], [13]. However, reasoning qualitatively
about the operation of a mechanism directly from its di
agram without the benefit of metric information (visuo
spatial reasoning) is a commonsense spatial reasoning ca
2Inquiries regarding this paper may be sent to the first author,
while questions about any particular model should be addressed to
the author of the corresponding section.
FISHWICK ET AL.: A MULTIMODEL APPROACH TO REASONING AND SIMULATION
ability that has not yet been automated. Consider, for
example, Fig. 1 from which the following questions can be
easily answered:
[Figure 1 about here.]
(1) If gear1 is turned clockwise, in which direction will
gear2 move? (2) Will the gear motions stop at some point?
Thus it appears that a qualitative characterization of the
spatial behaviors of a mechanism can, in principle, be gen
erated directly from its diagrammatic representation, with
out creating and using more complex geometric or algebraic
representations. There are however questions, such as what
the angular velocity of the lower gear will be if the upper
one is being turned at a certain velocity, which cannot be
answered from a diagram alone without additional metric
information. Nevertheless, a qualitative characterization as
above can be very useful in guiding more detailed analyses
of devices. Therefore, a model of visuospatial reasoning is
presented in the following two sections.
A. Problem Solving Strategy
A cognitive strategy for solving visuospatial reasoning
problems [14] involves the following activities. Informa
tion extraction: the diagram serves as a spatially organized
representation of information, and information is spatially
indexed and retrieved from it during problem solving. Pre
diction generation: predictions, based not only on infor
mation from the diagram, but also on conceptual infor
mation (e.g., rigidity of objects involved), are made about
how spatial interactions (such as a collision) affect object
behaviors. Visualizations of spatial behaviors: visualiza
tions of predicted behaviors are carried out using the dia
gram to discover their effects, which in turn generates more
predictions, and this drives the problem solving forward.
This strategy may be viewed as repeated cycles of analyze
visualizedetectpredict, in which the diagram is analyzed,
object behaviors are visualized, spatial interactions among
objects are detected, and their effects are predicted.
Consider the example of Fig. 1 again. The first step of
problem solving is to look at the diagram to comprehend
the geometry of the gear configuration and to note areas of
the diagram where objects are in contact or close proximity.
This visual analysis takes place through visual operations
such as scanning. Then, since the problem specification
includes an initial motion of gear1, a visualization of this
motion is performed. This visualization can be carried out
only until a spatial interaction is detected. This is because
an interaction among objects can potentially change the
way in which the configuration is evolving. So the visual
ization of gearl's rotation cannot continue after it is seen
to make contact with the lower gear.
We call object configurations with spatial interactions,
detected during visualizations, deliberative states. Delib
erative states contain object interactions which can affect
the object configuration's evolution by imparting motions
to previously stationary objects, arresting current motions,
or changing the nature of current motions. In order to pre
dict which of these changes, if any, will occur following a
deliberative state, deliberation or reasoning is required
hence the name. The occurrence, elimination, or change in
the nature of contacts between objects are typical interac
tions that signal a deliberative state. A deliberative state
triggers the transition of the problem solving process from
a visual phase (analysis and visualization) to a deliberative
phase (predictive reasoning).
The goal of deliberation is to predict what happens as a
result of the visualized object interaction. In the current
example this goal is to predict how the two gears will be
have as a result of their contact. The prediction that we
will make at this stage is that this contact will result in
the lower gear starting to turn counterclockwise in tan
dem with the rotation of the upper one. Note that in order
to make this prediction one requires three types of infor
mation. The first is information about the state of the
gear configuration when their contact was visualized. This
information is available from the visualization process in
volving the diagram. The second is conceptual information
that is not available from the diagram (such as the fact that
both gears are rigid). The third is information about how
objects behave in the physical world, in this case, that a
moving rigid object coming into contact with a stationary
rigid object tends to push the stationary one in the direc
tion of motion at the point of contact.
B. A VisuoSpatial Reasoning Model (VSRM)
What kind of a model should a reasoning and simula
tion system use for visuospatial reasoning? In answering
this question, we take a descriptive approach rather than
a prescriptive one. In other words, instead of presenting
a particular model, we describe desirable characteristics of
such a model along with suggestions derived from a specific
model that was recently developed [15], [14].
A VSRM needs to represent three types of knowledge.
First, there is spatial knowledge explicit in the diagram of
objects being reasoned about. Second, there is conceptual
knowledge about objects and their parts; information that
is relevant to reasoning, but which is not available from
the diagram. Third, knowledge that allows the model to
generate predictions regarding effects of spatial interactions
detected during visualization needs to be represented.
Let us first consider how diagrammatic information can
be represented. The structure of a representation should fa
cilitate operations to be performed on it. Visuospatial rea
soning requires three kinds of operations on diagrammatic
information. Two kinds involve access (and modification)
of diagrammatic information. One is spatiallyindexed ac
cess in which the accessed element satisfies some spatial
relation. An example of this is accessing any object that is
in contact with a given object in a configuration. The other
is objectoriented access in which the element satisfies some
nonspatial relation (e.g., partof). An example is access
ing the protruding tooth of gear2 from a representation of
Fig. 1. The third kind of operation is visualization which
transforms the representation to reflect the evolution of a
configuration due to object motions.
An array of cells (twodimensional for diagrams and
IEEE TRANSACTIONS ON SYSTEMS, MAN AND CYBERNETICS, VOL. XX, NO. Y, MONTH 1993
threedimensional for 3D images) is a representational
structure that is particularly amenable to spatiallyindexed
access. Each cell can contain one or more symbols repre
senting the part of the diagram which the cell covers. Such
arrays, called occupancy arrays, have recently been pro
posed as representations useful for computational imagery
[16]. Computer analogues of visual operations that humans
employ to achieve spatiallyindexed access, such as scan
ning and boundary following, can easily be implemented on
such arrays. An occupancy array facilitates visualization
as well, since array procedures to simulate the effects of ob
ject motions can also be designed easily. However, any high
resolution array representation of a diagram can have its
individual cells represent only small parts of contours in the
diagram being represented. This makes objectoriented ac
cess difficult since such access requires aggregation of sub
contours in a diagram into meaningful parts of objects in
the diagram. In other words, there is a mismatch between
the grain size required by objectoriented access and the
grain size of array cells. A solution to this problem is to
overlay a descriptive partof hierarchy on top of the array
representation. Such a composite representation consisting
of a descriptive hierarchy overlaid on a depictive array, as
illustrated in Fig. 2, is a suitable diagrammatic represen
tation scheme for a VSRM.
[Figure 2 about here.]
Conceptual (nondiagrammatic) information about objects
may be represented using frames which are linked by point
ers to the diagrammatic representation so that the reason
ing system can access the conceptual properties of an object
from its diagrammatic representation and vice versa.
Predictive knowledge knowledge that is utilized to
make predictions about spatial behaviors of objects sub
sequent to an interaction detected during visualization
is a critical part of a VSRM. It should combine both di
agrammatic information about the nature of the detected
object interaction and conceptual information about the
objects involved, in order to arrive at a prediction. This
is because spatial interactions between objects in diagram
matically identical configurations can have different effects
depending on conceptual properties, such as rigidity, of ob
jects involved. Furthermore, units of predictive knowledge
should be specified at an abstract enough level that these
have broad coverage. What constitutes predictive knowl
edge depends on the domain for which a VSRM is being
developed. For a 2dimensional blocks world domain [14],
representational units called . Id . have been used
to encode predictive knowledge. Fig. 3 shows a sample vi
sual case. A visual case has five parts: the prototypical
object configuration (POC) that the case represents, a de
scription (ED), visual conditions (VC) verifiable from the
diagrammatic representation, nonvisual conditions (NVC)
verifiable from conceptual knowledge, and predicted event
or events (P).
[Figure 3 about here.]
The model in [14] contains about seventy such cases cover
ing translation, rotation, sliding and tilting of objects.
Based on the aforementioned problem solving strategy, a
fourstage reasoning process can be designed for a VSRM:
analysis of diagrammatic representation, visualization of
motions, detection of deliberative states, and prediction of
spatial interaction effects. Fig. 4 shows the flow of control
among these stages.
[Figure 4 about here.]
The first stage is analysis of the diagrammatic represen
tation of the object configuration. One aim of this analysis
is to verify the feasibility of current predictions. Feasibil
ity verification is important because an effect, predicted in
the deliberative phase, of an interaction may not in fact be
feasible due to the influence of objects other than the inter
acting ones. For example, a collision, detected during vi
sualization, between a moving object and a stationary one
may generate a motion prediction for the stationary object
in the deliberative phase. But the stationary object may
already be obstructed by a third object, rendering the pre
diction infeasible. An analysis of the current configuration
can reveal such situations. The second stage, visualization,
involves transforming the diagrammatic representation in
accordance with how the object configuration will change
due to current motions.
Visualization is halted if and when an object interac
tion is detected. The configuration that the diagrammatic
representation depicts at this point is called a deliberative
state. Which types of object interactions are counted as
denoting a deliberative state depends on the domain and
class of problems for which a VSRM is being developed.
The model in [14] considers the following types of interac
tions as denoting a deliberative state: a collision between
objects, the removal of a previously existing interobject
contact, and a change in the nature of an interobject con
tact. When detected, these interactions will trigger a trans
fer of control to the deliberative phase. In this phase, the
type of detected interaction can be used to select applicable
subsets of predictive knowledge contained in the VSRM.
If visual cases are used to encode predictive knowledge,
their visual and nonvisual conditions can be used to se
lect, match and apply relevant cases. If the application
of predictive knowledge generates one or more predictions,
the control loop is reentered at the visual analysis stage.
The subsequent visualization will be guided by these new
predictions. This control loop repeats until the evolution
of the object configuration ceases or no more object inter
actions are predicted.
C. Summary
Visuospatial reasoning is a qualitative approach to di
agrammatically representable spatial reasoning problems.
It also provides a framework for integrating quantitative
methods [17]. Quantitative information can be represented
in a VSRM as part of conceptual information and quan
titative methods can be invoked during the deliberative
phase of reasoning. Two advantages of a VSRM, accru
ing from its use of diagrammatic representation of spatial
FISHWICK ET AL.: A MULTIMODEL APPROACH TO REASONING AND SIMULATION
configurations, are that (1) it can quickly provide plau
sible predictions regarding spatial behaviors of objects in
a configuration by directly manipulating its diagrammatic
representation instead of having to construct and use com
plex algebraic or geometric representations, and that (2)
such predictions can be used to guide the selective applica
tion of more complex spatial reasoning methods. However,
this model of visuospatial reasoning has some limitations.
Its reasoning strategy depends on the visualization using
diagrammatic representation being able to detect in the
correct order spatial interactions that may occur as an
object configuration evolves. But this is not possible if
the order depends on nondiagrammatic parameters such
as mass or acceleration. Also, arraybased representation
and visualization of threedimensional configurations can
become quite time consuming.
IV. FUNCTIONAL MODELING (FM)
A. Functional Modeling for Capturing Quantitative Rela
lionships
The goal of Functional Modeling (FM) is to make use of
the known purpose (or goal) of a device, to use that knowl
edge to organize causal understanding of the device, and to
provide a reasoning algorithm which can be used to simu
late the device given starting conditions. The roots of FM
lie in research by Sembugamoorthy and Chandrasekaran
which set the initial representational concepts for the func
tional point of view [18]. Sticklen and Chandrasekaran
applied and extended the initial work to include a simu
lation component to support diagnostic problem solving in
a medical domain [19]. Goel has used a simulation view
point to attack problems of design problem solving [20];
Punch has likewise used an FM simulation point of view as
a basis for the integration of Generic Tasks [21]. Allemang
has recently reported an application of the methodology of
functional representation to model computer programs [22].
Finally, Keuneke recently completed a research project in
which she demonstrated that the functional representation
is a valuable framework for the extraction of explanations
of diagnostic conclusions [23].
Overall, the functional viewpoint centers on enumerating
the proper primitives which can be used to organize causal
device understanding, and on working out algorithms for
utilizing the representation. Similarly motivated research
has recently been reported by Chittaro et al in Italy [24],
and by Franke at UTAustin [25]. In this section, we char
acterize a recent extension of the FM methodology to en
compass quantitative relationships between state variables
of a modeled device. This extension will be described via
our test bed example, the automotive cruise control device.
In research carried out in this test bed and fully described
in [26] we have found that the functional viewpoint can
be characterized as providing a framework for organizing a
series of quantitative calculations.
B. The Automatic Cruise Control System
The automatic cruise control (ACC) system is a hybrid
system that automatically controls the cruising speed of
the vehicle. It consists of electrical, electromagnetic, pneu
matic, and mechanical components. At the top level, the
ACC can be conceptualized as an equilibrium seeking sys
tem which tries to eliminate the difference between two con
trol signals: the commandspeed signal set by the driver of
the vehicle, and a signal indicating the vehicle's true speed.
The organization of the ACC is indicated in Fig. 5.
[Figure 5 about here.]
Representationally, the functional approach consists of
two sublanguages for device description: one sublanguage
for description of function, and one sublanguage for de
scription of behavior (i.e., a language of state variable
change). To solve the ACC representational problem, we
extended both sublanguages. The function sublanguage is
very simple, consisting of only three parts: a precondition,
a postcondition, and a pointer to "implementing behav
iors". Previously, we have represented the postcondition
in terms of the primitive ToMake (i.e., the action of this
primitive is to modify the value of a state variable of the
device). In the ACC example, we need another primitive,
one which will allow us to clearly indicate that the action
of a function is going to be to fix a state variable based
on the context of other state variable values at the point
at which the function is invoked. We have called this new
primitive of the function sublanguage ToCalculate. Cor
responding to the ToCalculate primitive in the function
sublanguage, we also required a similar new concept for
the state sublanguage. The representation of a behavior
in the FM approach consists of a graph structure in which
the nodes (after the first level nodes) represent statements
about changes of device state variables. Until our experi
ence with the ACC, these statements about state variable
changes were of two types: setting state variables to some
stated value, and incrementing state variables by some set
amount. To naturally represent the ACC we augmented
our sublanguage for state by allowing 1. ....i. I. i, ed state
. i .... in which a node in a behavior can be stated as
a numerical calculation over other variables of the device
which then sets a stated variable according to the result of
the computation.
The first step of the FM methodology is device decompo
sition. To represent the ACC, no extensions to our previous
work were needed to accomplish this step. The second and
third steps of the methodology are to represent the ab
stractly stated functionality that is known for each device,
which amount to listing its preconditions, postconditions,
and listing a pointer to its implementing behavior(s). The
third step of the methodology is to represent each behavior
as a state change graph such as shown in Fig. 10.
Let us begin with the highest level behavior of the cruise
control system, the adjustspeed behavior. As shown in
Fig. 6, if the speed of the car does not match the speed the
driver has set (i.e., if the error signal is not zero), then a
number of causal consequences will follow in a set sequence.
IEEE TRANSACTIONS ON SYSTEMS, MAN AND CYBERNETICS, VOL. XX, NO. Y, MONTH 1993
[Figure 6 about here.]
Note that by looking at one graphic (Fig. 6), it is possible
to grasp the overall operation of the cruise control sys
tem. The first causal consequence in Fig. 6 is that a new
value of the "duty cycle" is calculated. The reason that
causal consequence occurs can be ascertained by following
the link Make ThroftleControlSignal function of the control
electronics subsystem, which is shown in Fig. 7. Going to
a yet deeper level of detail, Fig. 8 shows the implementing
behavior makedutycyclebehavior.
[Figure 7 about here.]
[Figure 8 about here.]
There are several key points that should be emphasized
about the representation of the ACC that we have shown.
First, an FM representation is modular. Causality is rep
resented in small chunks that chain together via annota
tions of why one causal chain follows another. Second, an
FM representation I...l......, out" at a point that is ap
propriate for the problems the model must address. If our
model of a cruise control were to be used to trouble shoot
subchip level devices, then our representation would have
to be extended. As it stands now, we would be able to
model the ACC device to levels such as the OpAmp level
in Fig. 9. Third, the chunks are organized around mean
ingful concepts: the known functions of the device. Fourth,
the extensions which we have undertaken provide a highly
organized, and meaningful way of capturing causal knowl
edge about the ACC device.
[Figure 9 about here.]
We now move to the reasoning algorithm we have de
veloped to perform consequence finding over such an FM
representation. Space here precludes a detailed discussion
of our consequence finding engine, but it is fully described
in [19]. In synopsis, the reasoning algorithm first finds the
highest level function in the device which is applicable for
the stated boundary conditions of the problem. From that
high level behavior, a macroexpansion style of execution
proceeds to build up what we term the PSD the particu
larized state diagram so called because it is particularized
to the boundary conditions. Once one pass is completed of
this macro expansion of functions and behaviors, then the
process repeats until no functions of the system are appli
cable. Fig. 10 shows an example PSD after one cycle of
execution; Fig. 11 shows the PSD of the second cycle of
execution for the ACC.
[Figure 10 about here.]
Note that the vehicle speed has increased from the initial
condition (60 MPH) and is approaching the set speed of 65
MPH. Because the error signal is still not 0, the simulator
will remain active; it will repeat the same steps as before,
and will produce the values shown in Fig. 11 at the end
of the second invocation. It is important to note that the
PSD graph is not simply behavior graphs with all anno
tations removed. Each behavior begins with a number of
tests on state variables. During simulation, if a test on a
state variable fails, then the behavior in which that test
resides is not applicable, and will not become part of the
PSD. Thus the PSD is calculated only for the specific case
being examined (i.e., only for the stated initial conditions).
Although we do not further discuss it here, it is interest
ing to note that after the third simulation, since the error
signal is still not 0, the speed is over 65 MPH. In fact,
proceeding with the simulation produces a damped oscil
lating behavior. Although within our current framework
the FM simulator could not recognize and label the behav
ior as "damped and oscillating," it was very encouraging
to observe this result.
[Figure 11 about here.]
C. Functional Modeling in the MBR Landscape
Functional Modeling is best understood as an interme
diate type of reasoning between highly compiled level ap
proaches and naive physics approaches. The tasks of com
piled level problem solving is to relate associational knowl
edge directly to desired conclusions. For example, compiled
level classification for medical diagnosis relates observa
tions of patient states (signs and symptoms) to diagnos
tic categories. On the other hand, naive physics [27], [28],
[29] addresses the task of deriving the large scale behavior
of a device from the behaviors and connections of small
scale devices. For example, in the medical area, Kuipers
has developed a QSIMbased approach for modeling part
of kidney function from known small scale behavior.
Functional Modeling is intermediate between
associationbased reasoning (compiledlevel) and reasoning
aimed at deriving large scale behavior from small scale be
havior and connection (naive physics). The starting point
for developing an FM model is knowing a priori what the
functions (or purposes) of a device and its components are.
tFrom that knowledge, FM provides a framework for rea
soning towards particular performance of a device where
1 I i.. 11 ir" means with stated boundary conditions.
We have shown that with proper extension, we can utilize
FM as a framework for organizing numerical calculations
about a device. An apt question would be "Why can't nu
merical calculations about the ACC be expressed easily in a
simple Pascal program?" One reply to that question is that
yes, all the numerical calculations required to carry out the
solution of the ACC could have been done in Pascal, but
how well would such an approach scale? Suppose we were
representing a nuclear power plant. How difficult would it
be to develop a similar Pascal program in that case? The
reason that our FM approach to organizing numerical cal
culations will scale well is that the approach emphasizes (a)
modularity, and (b) an organization based around known
functionality of the device. In our approach, the numerical
calculations are simply ways of determining the results of
changes in state that are necessary to achieve known func
tionality. A crucial issue which any MBR technique must
face is the issue of "model selection." One of the reasons
that model selection is difficult is due to the multiple di
FISHWICK ET AL.: A MULTIMODEL APPROACH TO REASONING AND SIMULATION
mensions associated with the task. Along one dimension,
we must select the level at which we want to represent our
model. As Davis [30] points out, no model is complete.
The Functional Representation deals straightforwardly
with this fact by including the ability to point to ..11.1
L.... .. I,. as the reason for a given state variable transi
tion (in a behavior). This gives an ability to the modeler
to construct a model that I.. i.. , out" at whatever level
is appropriate. The issue of the type of model we want
to construct should be based on (a) the representational
primitives offered by a particular type of model, and (b)
the reasoning that a particular type of model enables. If
the knowledge we have of a device to be modeled can be
expressed in the primitives of a particular approach, and if
the output of reasoning with that approach matches what
we need to have in terms of output, then that particu
lar type of modeling approach would be a good candidate.
This statement may seem selfevident. Yet for the most
part, MBR has not dealt explicitly with issues of types of
models in these terms. We believe that one of the strongest
arguments supporting the FM approach to MBR is the rel
ative clarity of statement of the representational primitives
of the approach, and of the reasoning methods that come
with the approach.
D. Summary
Functional Modeling is a technique for organizing causal
knowledge about devices. That causal knowledge has been
extended (in the cruise control testbed) to include knowl
edge of quantitative relationships. In lineage, FM is largely
an outgrowth and extension of the qualitative reasoning
community, at least in terms of starting intuitions. How
ever, with the realization that its real power lies in orga
nizing device understanding for ease of use, new bridges
to other segments of the modeling landscape have become
possible. In particular, armed with the insight that the con
ceptual core of FM is not the distinction between qualita
tive and quantitative reasoning, it becomes again clear that
to develop robust models, multiple modeling approaches
are going to be necessary. In our own work at Michigan
State, we are now investigating the integration of bond
graph techniques and FM techniques. Our continuing goal
is to develop methods that will allow engineers and scien
tists to more easily develop, and share their understandings
of complex devices.
V. INTEGRATING QUALITATIVE AND NUMERICAL
SIMULATION MODELS (QQSIM)
A. Motivations
Numerical simulations support many engineering tasks
such as process monitoring and diagnosis, test of design pa
rameters, identification of critical situations, planning, and
scheduling. Usually, only specifically trained people can
interpret the results of numerical simulations. Moreover, if
the aspects of the system to be modeled are complex, both
the development of models and the simulation run time are
expensive in time and money.
To mitigate these problems, qualitative simulation [31]
has been proposed as an alternative way of describing the
behavior of a system. Qualitative variables may take a
value which belongs to a limited set of mutually exclusive,
rankordered symbols. The dynamics of variables is con
strained by relationships. Some of them are analogous to
the ordinary numerical ones, whereas others provide weaker
constraints. Criteria for the successful application of a
qualitative approach include:
only incomplete knowledge about a system is available:
therefore it is impossible either to identify quantitative
equations among variables or to find numeric values for
parameters and initial states;
the user is interested in a whole class of experiments,
instead of just the one produced by a numerical model;
the generalization of raw data at a higher level of
abstraction makes the decisionmaking process eas
ier [32].
In many engineering applications, a numerical descrip
tion of the behavior of the system is not needed: considera
tions about general trends can be successfully used to com
plete the given task. Moreover, the qualitative approach
makes it possible to do (usually) quicker and cheaper sim
ulations, producing qualitative descriptions of the states of
the simulated system, which can be interpreted with little
effort.
The wellknown drawbacks of the qualitative approach
arise from the impossibility to relate the simulation results
to the numerical values of the parameters. This produces
an exponential growth of the number of the possible states
the simulated system reaches. If quantitative information
is available, the evolutions of each variable are, in gen
eral, more constrained, possibly leading to a smaller set
of system behaviors. At the other extreme, quantitative
simulation produces just the behavior compatible with the
available numbers and numerical relationships.
Qualitative simulation of complex systems may generate
very large envisioning spaces. Here the advantages of qual
itative simulation drop: the program runs for a long time
and experts have to work hard to find the interesting behav
ior among the large number of possible states the system
may reach each one described by many variables. More
over, since the complexity of qualitative simulation usually
grows exponentially with the dimension of the model, some
applications cannot even run on the available machines.
Here, we present a method to integrate these two model
ing paradigms, enabling a reuse of existing numerical mod
els. The method has been implemented in QQSIM [33], a
system running in Common Lisp and CLOS.
B. Basic assumptions
We assume that the system to be modeled can be parti
tioned in two parts: one described qualitatively and the
other one numerically. The quantitative model is de
fined in terms of a set QT = {Qi, ..., Qtn} of quantita
tive variables, and the qualitative model in terms of a set
QL = {Ql, ..., Qlm} of qualitative variables, where the set
QTL = {Qt.., QI, lp} of the socalled shared variables is
IEEE TRANSACTIONS ON SYSTEMS, MAN AND CYBERNETICS, VOL. XX, NO. Y, MONTH 1993
bijectively mapped both onto a subset { Qi, ..., Qti+p} of
QT and onto a subset {Qlt, ..., Qlt+p} of QL. Therefore,
the variables of QTL admit a double representation: one
on quantitative and the other on qualitative terms.
Both the models (qualitative and quantitative) are used
for a parallel simulation, where the numerical evolution of
the shared variables is qualitatively interpreted and used to
prune the incompatible qualitative behaviors. As a conse
quence, the results from qualitative simulation contain also
quantitative information about both time and variable val
ues.
This approach can be used to answer questions such as:
Which states will the system reach, given the initial
conditions?
What will be the value of variable X at time TP
When will variable Y reach the value Y ?
QQSIM may provide either qualitative or quantitative
answers to the second and third questions above, depend
ing on the ongoing simulation and the underlying models.
For instance, if time T is exactly the time to which some
of the shared variables reached a limit point, the answer
to the second question will be the numerical or qualita
tive value of variable X at that time, depending to which
of the two models X belongs. Otherwise, time T will be
compared with the available time labels, and the returned
values of X will be the ones of the states whose time labels
are qualitatively compatible with T.
C. Definition of Models
Two models are used in QQSIM: a numerical model and
a qualitative one. The numerical model is a standard model
used for numerical simulation. We would like to stress the
fact that our approach can be applied to already existing
numerical models, to enrich them with qualitative consid
erations. Required properties for the numerical model are:
the numerical simulation has to produce a temporally
ordered sequence of values for the variables in the
model;
it should be possible to stop and restart the numeri
cal simulation whenever the synchronization algorithm
requires it;
the sampling frequency should be high enough to avoid
the presence of two limit points (i.e. maxima, zeroes,
or minima) in the same interval. This requirement is
usually weaker than those usually taken in numerical
simulation, so we assume that it is always satisfied.
The qualitative model is expressed using the standard
QSIM elements including qualitative variables and con
straints. Qualitative variables, identified by a label, may
take a qualitative value, which is a pair < value, trend >,
where value is one element of the set {+, 0, }, and trend
is an element of the set {INC, DEC, STD}. Each pair
< value,trend > is associated to a landmark (or to an
interval between landmarks) where it holds. Landmarks
are represented by labels and form an ordered set. As in
Q3 [34] [35], landmarks can be associated to actual numer
ical values. Constraints among variables state algebraic
(ADD, MINUS, MULT), derivative (DERIV), and qualita
tive (M+) relationships.
The simulation generates states that the system may
reach. Each state consists of a set of values one for each
of the qualitative variables and a time label, expressing
a value belonging to the numerical simulation time axis
when the state is reached. This label can be computed
only when at least one of the shared variables reaches a
limit point in the present state, since only in this case do
we know exactly from the numerical simulation when this
event happens.
The numerical simulation may also supply numerical val
ues for landmarks present in the values of the shared vari
ables.
D. Model Interfacing
The two models are integrated by the simulation process.
First the initial conditions for both the models are checked
for consistency. Then, the numerical model is started, pro
ducing values which are monitored for a qualitatively sig
nificant change. Numerical value sequences for the shared
variables are translated into qualitative terms. When a
shared variable reaches a limit point, the numerical simu
lation is halted.
The (QTLprocess) is performed in two steps. During the
first step, each qtli is analyzed in its trajectory, indepen
dently from that of the others. Its qualitative behavior is
identified, along with the corresponding limitpoints. This
identification is based on the successive sampled numerical
values as proposed by the quantitative simulation.
For instance, if at time Ti variable qtll takes on the
value of 20 and at time T2 it takes on the value of 21, its
qualitative behavior will be (< Ti, T2 > (pos, inc)), which
has to be read "in time interval < T, T2 > qtll is positive
and incrementing."
Inferential steps might be required: for instance, when a
(pos dec) follows a (pos inc) interval, a (pos std) has to be
interposed to preserve qualitative continuity. These infer
ences are based on a 9 x 9 table, mapping all the possible
qualitative states for a variable onto subsequent variable
states. Acceptable sequences, impossible ones and inter
polations thus become identifiable. Having detected the
behavior of adjacent intervals, a second table defines the
behavior in the intermediate points.
The second step of the QTLprocess involves a synchro
nization of the shared variables. With our assumptions on
the sampling rate, variables having limit points in adjacent
intervals may be actually related so as to have limit points
formally coinciding. This is the case for a variable and its
derivative, or the case of two variables differing by a con
stant. The exact location of maxima and minima for each
sampled variable is not definite: a maximum is located on
the basis of three points, the middle one with the highest
of the three values (the lowest in case of minimum). It is
therefore possible that the exact location of the maximum
falls in the preceding or in the subsequent interval. This de
pends on the particular sampling used. The determination
of the exact location of the limit point is arbitrary, since
FISHWICK ET AL.: A MULTIMODEL APPROACH TO REASONING AND SIMULATION
it is only based on the sample points, but it is important
for the qualitative states generated, since the distinctive
time points are placed by QSIM in correspondence to the
limit points. Therefore, the fact that two variables have
limit points in the same interval or in different intervals
corresponds to the generation (or acceptance) of a differ
ent number of qualitative states.
We devised an algorithm working on all the qtli, which
resolves the attribution of the minima/maxima position to
an interval. It is based on the assumption that the possi
bility to attribute limit points of different variables to the
same interval could show a relationship among these vari
ables. This relationship would be lost if we consider their
trajectories as independent. For instance, in the case of a
variable and its derivative, if we attributed the maximum
of the variable to a time interval adjacent to the one of
the zero of its derivative, then the constraint of qualitative
derivation existing among them would not be satisfied.
However, our algorithm might synchronize unrelated
variables: this does not mean that it forces a relationship
(possibly nonexistent) among the synchronized variables,
since the attribution of the limit point to one of the two
possible intervals is arbitrary. The synchronization algo
rithm is one way to solve the ambiguity of the assignment
of the position in time of the limit point. Its effectiveness
comes from our assumption that the duration of the simu
lation step is very short with respect to the characteristic
times of the modeled variables, so that the probability for
two unrelated limit points to be contemporary is negligible.
Now, let us continue the description of the simulation
process. The qualitative values so obtained for the shared
variables are used as additional constraints to generate the
next states the system can reach from the already identi
fied ones. Therefore, the number of new states is cut by
information coming from quantitative simulation. Then,
the numerical simulation is started again, and it runs until
a new qualitative state is reached by a shared variable.
This process is iterated until no more new states can be
generated, or the limits imposed by the user are reached.
E. Summary
The QQSIM approach is useful whenever:
the numerical model of a complex system is already
available;
there is the need of making some modifications to this
complex system, or to add parts to it;
the modifications or the added subsystems can be rep
resented by qualitative, constraintbased models;
the user would like to have an envisioning tree describ
ing all the possible states the whole system reaches
given some initial conditions.
The numerical information is used as a filter for the en
visioning activity, thus contributing to reduce the combi
natorial explosion affecting this type of simulators.
The QTLprocess defines a relationship between a land
mark of a shared variable and the value it takes on at the
limit point. Therefore, the envisioning tree may contain
states enriched by information about the actual values of
the shared variables.
Time quantification also has a special relevance, since
the qualitative time axis is common to all the qualitative
variables and a total order of the time points at which they
reach their limit points is defined on it. QQSIM establishes
a relationship between real and qualitative time for the
states where shared variables undergo a variation. There
fore, it is possible to have an intervalvalued time measure
for the unshared variables. This is also a significant en
hancement with respect to the standard QSIM approach.
VI. MULTIMODEL INTEGRATION3 (MI)
A. Overview
Simulation methodology has developed concepts to
model complex systems over multiple levels of abstrac
tion [37], [38], [39]. Oren [40] has developed the defini
tion of multimodel4 to formalize models containing sev
eral submodels, only one of which is put into effect at any
time. Other groups in the AI community have also ad
dressed the use of multiple models to support multilevel
reasoning architectures [24], [41], [42]. Cellier [43] devel
oped an approach to combined continuous/discrete event
models implemented in a GASP language extension. Prae
hofer [44] extended the Discrete Event System Specification
(DEVS) [8] to provide a formalism and a simulation envi
ronment for specifying combined continuous/discrete event
models. In this section, we build on these developments
by providing a methodology and formalism for developing
multilevel, cooperative models of physical systems of the
type studied in qualitative physics. The formalism should
help to build reasoning and simulation systems that use
multiple models at different levels.
We will use a system of boiling water to illustrate our
methods (see Fig. 12.
[Figure 12 about here.]
Although at first glance it appears too simplistic, the boil
ing water system is appropriate for demonstrating a wide
range of discrete and continuous behaviors as well as lev
els of abstraction. All models for computer simulation are
constructed to answer a certain class of questions. With
our multimodel approach, we are capable of answering a
larger number of questions than with a singlelevel model.
For instance, the question "How long will it take for the
pot to boil over?" requires a numerical answer whereas
"What is the next step after water starts heating?" in
volves a qualitative answer such as "If the system is in the
phase heating, and the control knob is turned off then the
next phase will be cooling. However, if the water tempera
ture reaches 100 then the water starts boiling." We present
a method that permits this kind of multilevel reasoning.
Fishwick and Zeigler [2] have recently discussed a method
3The study described in this section is an extension of material
drawn from two sources [36], [2].
4Our concept of multimodel, as in the title of this paper, includes
multiple independent models as well as models containing submodels
in a hierarchy. It is a more general notion than Oren's multimodel.
IEEE TRANSACTIONS ON SYSTEMS, MAN AND CYBERNETICS, VOL. XX, NO. Y, MONTH 1993
for linking the heterogeneous level coupling concept within
a DEVS framework.
B. Combined Models
Taking the cross product of time and state in terms of
two possible values ("discrete" and "continuous") suggests
four possible model types. The Discrete Event model type
has continuous time and a discretized state space. A Dis
crete Time model has a discrete time space with equal time
intervals (the state space may be either discrete or continu
ous). A Continuous model has continuous time and space.
Table I displays these combinations with example model
formalisms for each. What about continuous events? In
the simulation literature [45], [46], one finds reference only
to discrete events. Continuous events might be defined in
terms of the start and end of an arbitrary numerical in
tegration interval. However, this concept is not adequate
since it depends on a simulation process, and is not an in
trinsic characteristic of the model. It seems that events, by
their very nature, are discrete since they map to cognitive
and linguistic concepts connected with the processes that
we model. In the next section, we attempt to provide a
conceptual framework for understanding discrete events.
[Table 1 about here.]
A combined model combines two or more of the
above model types. For instance, a combined discrete
event/continuous model has two distinct model types: a
discrete event model and a continuous model. These two
models are coupled with discrete events [43], [44].
C. Multimodels
Consider a pot of boiling water on a stovetop electric
heating element. Initially, the pot is filled to some prede
termined level with water. A small amount of detergent is
added to simulate the foaming activity that occurs natu
rally when boiling certain foods. This system has one input
or control the temperature knob. the knob is considered
to be in one of two states: on or off (on is 1900C; off is a 
ambient temperature). We make the following assumptions
in connection with this physical system:
1. The input (knob turning) can change at any time.
The input trajectories are piecewise continuous with
two possible values (ON,OFF).
2. The liquid level (height) does not increase until the
liquid starts to boil.
3. When the liquid starts to boil, a layer of foam in
creases in height until it either overflows the pot or
the knob is turned off.
4. The liquid level decreases during the heating and over
flow phases only.
To create a mathematical model, we must start with
data and expert knowledge about the domain. If enough
data can be gathered in a cost effective way then our
model engineering process will be simplified since we
will not have to rely solely on heuristics to identify
the model. By analyzing a pot of boiling water we
may derive simple causal models whose individual tran
sitions may be knobon 4 watergettinghotter(1.0) or
water getting hotter 4 water_boiling(0.75) where num
bers in parentheses are certainty factors. An important
facet of system modeling is that we choose certain modeling
methods that require a categorization of informally spec
ified system components. Key components of any system
model are input, output, state, event, time and parameter.
Different modeling methods include these components in
different ways. For instance, an FSA focuses on stateto
state transitions with input being labeled on each arc. A
dataflow model, on the other hand, focuses on the transfer
function between input and output. Homogeneous model
refinement [2], [3] is the process of refining models of the
same type. For instance, we might represent the boiling
water system using a hierarchy of finite state automata
(see Fig. 13). The three levels are labeled FSA1, FSA2
and FSA3.
[Figure 13 about here.]
Heterogeneous refinement takes homogeneous refinement
a step further by loosening the restriction of equivalent
model types. We might have a Petri net at the high ab
straction level and we may choose to decompose each tran
sition into a block graph so that when a transition fires
within the Petri net, one may "drop I.. into a func
tional block level. For the FSAs in Fig. 13 we choose to
represent each state as a continuous model. Specifically,
each state will define how three state variables, T (temper
ature), Hw (height of water), and Hf (height of foam on
the top of the water) are updated. In all cases, Hf > Hw.
The end result will eventually be a multilevel model that
will be coordinated by the FSA hierarchy.
Fig. 14 displays a block diagram of heating within the
heating state. Proper coupling is essential in heteroge
neous refinements. That is, it must be made clear how
components at one level match components at the higher
level. Note, in Fig. 14, the transfer function taking the
ON/OFF input detected by the FSA and converting these
input values to temperature values for the block network.
Specifically, the block labeled 'F' performs the mapping
from 'ON/OFF' to realvalued temperatures a < T < 100.
Due to the latent heat effect, T of water cannot exceed
100 unless all the water has vaporized. After all of the wa
ter has turned to steam, the temperature increases beyond
100; however, the system passes to the underflow state in
our model since Hw = 0.
[Figure 14 about here.]
The lowlevel continuous models M, ..., M6 are defined as
follows:5
1. (Mi) COLD: T H = 0, Hf = 0.
2. (M2) HEATING: T = ki(100 T), Hi = 0, Hf = 0.
3. (M3) COOLING: T= k2(a T), Hw = 0, Hf = k3.
4. (M4) BOILING: T = 100, H, = k4, Hf = k5.
Models M2 and M3 exhibit first order exponential behaviors and
are, therefore, rough approximations of the actual boiling water
system.
FISHWICK ET AL.: A MULTIMODEL APPROACH TO REASONING AND SIMULATION
5. (M5) OVERFLOW: same as BOILING with con
straint Hf = Ht.
6. (M6) UNDERFLOW: T = undefined, H, = Hf =
0.
The system phase is denoted by 4 and the state variables
are:
T: temperature of water.
H,: height of the water.
Hf: height of the foam.
Note that the continuous models share a common set of
state variables. However, in general state variables may be
different for each Mi model.
There are also some constants such as Ht for the height
of top of pot, H, for the starting height of water when
poured into the pot; and ki rate constants. The initial
conditions are: 1 = cold, T(0) = a, H,(0) = Hf(0) =
H, and knob = OFF. By including the functional block
knowledge, we create one large model called COMBINED
that is defined as the fully expanded FSA3 level with each
state containing a block model (as in Fig. 14).
D. Summary
The multimodel approach is one where models of differ
ent types are connected together in a mi...1. ." fashion.
This approach yields more choices to the model design
ers who are now able to pick a model type to support a
level of system abstraction. High levels of abstraction (in
Fig. 13, for instance) can be used to reason about the sys
tem, whereas low levels (defined by differential equation
sets) are useful for results requiring a smaller amount of
granularity in terms of specification and explanation.
VII. RELATING THE APPROACHES
We have described four methods for promoting the mod
eling of dynamical systems and reasoning about them at
different levels. Each approach addresses the multiple
model problem from a different perspective. These perspec
tives are outlined in table II so that individual approaches
can be better compared and contrasted. Note the follow
ing terminology and abbreviations used in table II. The
approaches (VSRM,FM,QQSIM,MI) appear in the same
order presented within the paper. All physical phenomena
can be studied with regard to their geometry (connectiv
ity) or dynamics. Dynamic models all have the following
components: (1) state/event space, (2) time space, (3) pa
rameter space, (4) input/output space and (5) the type
of relations or functions used to link the first four spaces
together. This categorization is in accordance with the
basic concept of system [47]. The components of a geo
metric model are the representational structure (struc) it
uses and operations (oper) provided on this structure. By
crosscorrelating the four approaches with their dynamic
and geometric facets, we can obtain a grasp of how the
four methods are situated with respect to one another. The
term symbolic refers to a nominal value such as a proposi
tion in logic or natural language expression, real refers to
a ratio variable implemented as a floating point value, in
terval refers to an interval with realvalued endpoints, and
fuzzy refers to a fuzzy number.
[Table 2 about here.]
Now, let's discuss each approach and its unique contribu
tion. VSRM tackles the problem of representing spatial
dynamics and geometry. The geometry is represented in a
symbolic array. The spatial dynamics is represented and
reasoned about by transforming this array in accordance
with predictions derived from production rules. FM ad
vocates the use of causal graphs as the primary medium
of dynamic representation since causal graphs often corre
spond to the purposes or goals that a system is designed to
achieve. QQSIM represents two levels of abstraction: qual
itative and quantitative. During simulation, ambiguity of
relationships among state variables and parameters at the
qualitative level is reduced by a search at the quantitative
level. MI does not focus, particularly, on a given modeling
method. Instead, the emphasis is in how to integrate exist
ing models so that one can switch levels during reasoning
and simulation.
What are the key differences among the four approaches?
There are three items that reflect a distinction:
Measurement: At what level is a variable known? Does
a value come from a sensor or what a human com
municates in natural language? If a variable can be
physically measured then we need to know the level
of granularity associated with the measurement. Of
ten, the scales of nominal, interval and ratio suffice.
Nominal scales are used in AI to represent proposi
tional knowledge about devices assuming that physical
measurements are not obtainable or too expensive. If
data are available in the form of floating point values
(often through sampling using an analog/digital inter
face) then we will use these. The issue, though, is not
always one of expressiveness and measurement scale.
It is often computationally more efficient to compute
values through logical inference than through numer
ical methods. Computational efficiency is not always
a result of using qualitative methods, though when
we make the functional relationships among state vari
ables ambiguous (by saying, for instance, that a func
tion is monotonically increasing or decreasing with
out any further specification) then we are forced to
search over a predefined function space that is sub
ject to combinatorial explosion. In any case, we have
learned that one must be careful about the level chosen
in representing variables; in determining what mea
surement scales are appropriate. VSRM uses a fairly
high level scale nominal since it uses only symbolic
knowledge. The other three approaches admit all three
scales. Both VSRM and FM do not explicitly repre
sent a time line6, so trajectory information for states
are not obtainable. The QQSIM and MI approaches
have time bases. These focus more on simulation and
less on reasoning unlike VSRM (which supports rea
soning about processes) and FM (which supports cal
6In FM, work in another application domain endows FM with the
capability to reason over time [48].
IEEE TRANSACTIONS ON SYSTEMS, MAN AND CYBERNETICS, VOL. XX, NO. Y, MONTH 1993
culating new states from old ones).
Geometry C Dynamics: Comprehensive approaches to
systems study will eventually require representations
that combine geometry and dynamics. VSRM is a
push in this direction whereas the other approaches
focus completely on dynamics. Multiple modeling ap
proaches should attempt to incorporate both types of
models in future since this enlarges the base of ques
tions that can be asked of a system. We view the
convergence in dynamical and geometric representa
tions as being similar to the ongoing research in inte
grating computer aided design (CAD) and computer
aided manufacturing (CAM) modeling techniques.
Perspectives & Levels: QQSIM proves that symbolic
and numerical perspectives need not be considered in
exclusion of each other. To be most productive, future
toolkits for analyzing systems must incorporate more
than one level. The QQSIM and MI approaches ad
dress this issue of multiple levels by explicitly support
ing more than one representation language, while the
FM approach suggests one specific modeling language
that admits multiple levels. The VSRM approach does
not address this issue.
In a nutshell, VSRM shows how predictive knowledge
about dynamics and a "... I. II. representation of ge
ometry can be used together for reasoning about spatial
dynamics. FM promotes the organization, based on the
notion of teleology, of knowledge about causal dynamics of
engineered systems since this bears a close relationship to
the way that humans design and reason about such sys
tems. QQSIM shows how qualitative and quantitative lev
els of representation and simulation can be integrated. MI
provides a formal definition of how to integrate existing
model types together into a unified framework with multi
ple abstraction levels.
One lesson to be drawn from this paper is that build
ing the model of a system to support both simulation and
reasoning can be approached from two directions. One
is topdown, in which a hierarchical and modular model
is developed, whose levels reflect a systemsubsystem de
composition organized around their intended functions and
designed behaviors to achieve these functions (FM) or a
statespace decomposition organized in terms of finite state
automata (FSA) whose states expand into other FSAs or
block models (MI). The other is bottomup, in which spa
tial subsystems are represented in terms of their geometry
and predictive rules that govern their behavior (VSRM)
while nonspatial subsystems are represented in terms of
relevant qualitative/quantitative variables and constraints
(QQSIM). The topdown approach provides a framework
for guiding simulation, controlling its level of detail, and
interpreting simulation results in terms of intended func
tions and expected state transitions. The bottomup ap
proach is useful in detecting new behaviors resulting from
unforeseen interactions (interactions among state variables
or spatial interactions among components). Hence a multi
model that combines both will be well suited to simulating
and reasoning about both designed and unexpected behav
iors of a system.
We will now discuss two of the application examples men
tioned in the paper to illustrate how the four approaches
could be used together. Consider a variation of the gear ex
ample in Fig. 1, in which there are two pins between which
the protruding tooth of gear2 oscillates as the driving gear
(gear1) alternatingly rotates in opposite directions. It can
be easily imagined as part of a more complex mechanical
device such as a clock. The FM approach allows a model
of such a device to be built, so that its purpose is linked
to the functions of its components and mathematical com
putations (such as those involving gear ratios) are modu
larly organized within this teleological framework. Orthog
onally, a hierarchical FSA model of this device can also be
built as per the MI approach, which facilitates reasoning
about state transitions of the device at different levels of
abstraction. If a capability for detailed simulation is re
quired however, the model also needs to represent how each
component constrains the motions of others. Geometric
constraints due to component shapes can be captured in
a VSRM. But differential constraints among dynamic vari
ables that take numerical values (e.g., torque, velocity, and
acceleration) or qualitative values (e.g., the position of the
protruding tooth of gear2 may have only two qualitative
values of interest: touching pin1 or touching pin2) are
best represented using the QQSIM approach. These four
approaches together thus allow a comprehensive model of
the device to be built.
Consider the automobile cruise control (ACC) system
of Fig. 5. Its components have intended purposes (func
tionalities). So the functional modeling approach (FM)
can provide a model which links the functions of the sys
tem to the functions of its components and their behav
iors. As discussed in Section 4, these behaviors can be
further refined into mathematical equations, thereby pro
viding a framework for organizing mathematical models.
However, reasoning about the function of a system compo
nent with spatial behaviors like the throttle actuator
requires a model such as the visuospatial reasoning model
(VSRM). Similarly, there is sometimes a need to reason not
only about the intended function of a system or a compo
nent, but also about all possible states it can reach from
certain initial conditions. If such reachability information
(or "envisionment") needs to be generated, qualitative and
numerical simulation models, and their integration as dis
cussed in Section 5 (QQSIM), should be made parts of the
overall model. The multimodel integration approach in
Section 6 (MI) provides an orthogonal modeling approach
which supports user queries at different levels of abstrac
tion. System components, like the control electronics mod
ule of the ACC, that involve both discrete and continu
ous processes can be modeled with this approach. Thus,
a complex system such as the ACC can be modeled com
prehensively by (1) developing an overall functional model
(FM), (2) creating visuospatial models of spatial subsys
tems (VSRM), (3) specifying constraints relating numerical
and qualitative parameters and state variables and devel
oping a corresponding qualitative/quantitative simulation
FISHWICK ET AL.: A MULTIMODEL APPROACH TO REASONING AND SIMULATION
model (QQSIM), and (4) using the multimodel integration
approach to integrate a hierarchy of model abstractions
(MI).
We have presented four different approaches to improve
modeling of dynamic systems. These four models are
drawn from different disciplines: Systems and Simulation
Theory, Artificial Intelligence and Cognitive Science. This
is an interdisciplinary effort that began at a joint confer
ence. We have now taken the next logical step con
structing a paper that presents methods, in service of the
common goal of modeling, from researchers in each disci
pline. As we collaborate in this manner, we find ourselves
closely examining each others' terminology, methods and
motivations. For the future, we hope that this kind of inter
disciplinary effort will foster further collaborations among
ourselves as well as other workers in the field.
ACKNOWLEDGMENTS
Dr. Fishwick would like to acknowledge partial research
support from a Florida High Technology and Industrial
Council (FHTIC) grant entitled "Real Time Computer An
imation for Interactive Visualization." Material in Sec
tion 3 is based on research conducted at the Laboratory
for Artificial Intelligence Research, Ohio State University,
and supported by grants to the laboratory from ARPA
(under AFOSR contract I I 1.'l89C0110) and British
Petroleum. Dr. Narayanan acknowledges Hitachi Ad
vanced Research Laboratory for facilitating the prepara
tion of this paper. The analysis and implementation of the
cruise control system (in the section on Functional Mod
eling) was carried out under Dr. Sticklen's supervision by
Mr. Ahmed Kamel. Dr. Sticklen's research at Michigan
State is supported by ARPA (ARPA 8673), the NSF Center
for High Speed, Low Cost Polymer Composites Processing
at MSU, the McDonnell Douglas Research Foundation, the
State of Michigan Research Excellence Fund, and generous
equipment support from Apple Computer. Research of Dr.
Bonarini (QQSIM) has been supported by the Italian Na
tional Research Council (CNR) as part of the Progetto Fi
nalizzato Informatica e Calcolo Parallelo. The research has
been done with Vittorio Maniezzo, and QQSIM has been
implemented by Massimo Pianciamore, who also gave con
tributions to the theoretical aspects.
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Paul A. Fishwick is an associate professor
in the Department of Computer and Informa
tion Sciences at the University of Florida. He
received the BS in Mathematics from the Penn
sylvania State University, MS in Applied Sci
ence from the College of William and Mary,
and PhD in Computer and Information Science
from the University of Pennsylvania in 1986.
He also has six years of industrial/government
production and research experience working at
Newport News I, I ..I I..... and Dry Dock Co.
(doing CAD/CAM parts definition research) and at NASA Langley
Research Center (studying engineering data base models for struc
tural engineering). His research interests are in computer simulation
modeling and analysis methods for complex systems. He is a senior
member of the IEEE and the Society for Computer Simulation. He is
also a member of the IEEE Society for Systems, Man and Cybernet
ics, ACM and AAAI. Dr. Fishwick was chairman of the IEEE Com
puter Society technical committee on simulation (TCSIM) for two
years (19881990) and he is on the editorial boards of several journals
including the ACM Transactions on Modeling and Computer Simu
lation, IEEE Transactions on Systems, Man and Cybernetics, The
Transactions of the Society for Computer Simulation, International
Journal of Computer Simulation, and the Journal of Systems Engi
neering.
N. Hari Narayanan is a visiting research sci
entist at the Advanced Research Laboratory of
Hitachi Ltd. His doctoral research was con
ducted at the Laboratory for Artificial Intel
ligence Research, Ohio State University. He
also holds degrees in Computer Science, Au
tomation, and Electrical Engineering from the
University of Rochester, Indian Institute of Sci
ence, and Birla Institute of Technology and
Science respectively. His main interest is in
investigating the role of perceptual represen
tations in reasoning and problem solving, from both computational
and cognitive perspectives. His current work is on the problem of
behavior hypothesis from device diagrams. He is also interested in
qualitative spatial reasoning and modelbased approaches to diagno
sis and design. Dr. Narayanan organized the 1992 AAAI Spring
Symposium on Reasoning with Diagrammatic Representations, and
has guestedited a forthcoming journal special issue on "computa
tional imagery" (Computational Intelligence, Vol. 9, No. 3). He
is currently editing a book on reasoning and problem solving with
diagrams. He is a member of AAAI and ACM.
Jon Sticklen is Associate Professor of Com
puter Science and Director of the Intelligent
Systems Laboratory, Michigan State Univer
sity. Following his Ph.D. studies at the Ohio
State University, Dr. Sticklen joined the fac
ulty at MSU where he initiated an active re
search program in knowledgebased systems.
Sticklen's major research foci are in integrative
approaches to large grain task specific prob
lem solving, functionbased reasoning, and the
theory of knowledgebased systems. Sticklen
and his associates are currently engaged in a wide variety of domain
projects including the design and fabrication of polymer composite
materials, the modeling of landscape level ecological systems, and the
development of decision support software for managing production
agriculture in the lower Nile valley.
Andrea Bonarini was born in Milan in 1957.
He received his Laurea (Master of Technology)
in Electronics Engineering, in 1984, and his
PhD in Computer Science in 1989, both from
the Politecnico di Milano, Italy. He is Tenurial
Assistant Professor at the Department of Elec
tronics and Information of the Politecnico di
Milano. Since 1984, he is member of the Po
litecnico di Milano Artificial Intelligence and
Robotics Project. He is founding member of
the AI*IA (the Italian Association for Artifi
cial Intelligence), and cofounder of the AI*IA Special Interest Group
on Qualitative Reasoning. He took part to several CEC Projects
(within the ESPRIT and EUREKA programmes ), and to several
National Research Projects. His research interests are in the field
of Uncertainty Representation, applied to Modelbased Diagnosis of
industrial plants, Simulation, and Control, with special emphasis on
fuzzybased technologies. He is also working on Reinforcement Learn
ing techniques for the automatic synthesis of Fuzzybased systems.
FISHWICK ET AL.: A MULTIMODEL APPROACH TO REASONING AND SIMULATION 15
LIST OF FIGURES
1 A configuration of two interacting gears .................. .................. 16
2 A diagrammatic representation ................ .................. . . . 17
3 A visual case . . . . . . . . . . . . . . . . . . . . . .. . . . 18
4 Stages of visuospatial reasoning .................. .................. . . 19
5 Cruise control system scheme atic. ............... .................. . . . . 20
6 A top level behavior of the cruise control system. .................. ............. .21
7 A function M akeThrottleSignal. .................. ................... .. . 22
8 A behavior m akedutycycle. .................. ................... ... . 23
9 A low level behavior amplifybehavior .................. ................... 24
10 State variables after one ... ... i .11.. ................ ................. ... 25
11 State variables after two .. .... 1 i..... .................. ................... 26
12 A pot of boiling water. .... ... .... ... .... ... .... ... .... ... .. ........ 27
13 Homogeneous FSA refinement. .................. . ................... ..... 28
14 Decomposition of heating state. .................. ................... ... . 29
IEEE TRANSACTIONS ON SYSTEMS, MAN AND CYBERNETICS, VOL. XX, NO. Y, MONTH 1993
pin
Fig. 1. A configuration of two interacting gears
FISHWICK ET AL.: A MULTIMODEL APPROACH TO REASONING AND SIMULATION
device
 T 
cylinder piston
/
I 
flywheel
s\
le
inlet outlet cvityhead hinge r6d hige rim a]
I I I t
,I / i \
I I
sI I I
I I I I
\ I
' /L
I '!    I I  ^
;.' m T ^ ^\ *
Fig. 2. A diagrammatic representation
array
IEEE TRANSACTIONS ON SYSTEMS, MAN AND CYBERNETICS, VOL. XX, NO. Y, MONTH 1993
O.F.p
O.F.d 0F
O.h
0
0.RMA
An impetus acting on a rigid hinged object at a location such that
ED the object's hinge is to the left of the impetus direction can produce
a counterclockwise rotation of the object about its hinge.
O.F(O.F.p, O.F.d);
VC
ImpetusDirectionRelativeToHinge(O.F.d, O.F.p, O.h)=Left;
NVC Object(O); Rigid(O); Hinged(O);
P O.RM such that O.RM.h=0.h and O.RM.d=Counterclockwise;
Fig. 3. A visual case
POC
O.h
0
FISHWICK ET AL.: A MULTIMODEL APPROACH TO REASONING AND SIMULATION
Scan the diagrammatic representation
to note interobject contacts, etc.
Confirm feasibility of the latest predicted
motion.
ANALYSIS
Visualize the motion by incrementally
transforming the diagrammatic representation.
VISUALIZATION
Watch out for interactions among objects.
n
DETECTION
Use characteristics of the current object configuration
and conceptual information to locate, retrieve, and appl4
relevant predictive knowledge; generate predictions.
PREDICTION
Fig. 4. Stages of visuospatial reasoning
,epactions
detected
I
HALT
IEEE TRANSACTIONS ON SYSTEMS, MAN AND CYBERNETICS, VOL. XX, NO. Y, MONTH 1993
Control Electronics
Fig. 5. Cruise control system schematic.
FISHWICK ET AL.: A MULTIMODEL APPROACH TO REASONING AND SIMULATION
errorsignal # 0
*** Using function of
*controlelectronics*
MakeThrottle ControlSignal
Calculate dutycycleofthrottlecontrolsignal
*** Using function of
*throttleactuator*
ControlThrottle Position
Calculate enginethrottleposition
*** Using function of
*enginedrive*
DriveVehicle
Calculate vehiclespeed
I* Using function of
*speedsensor*
ConvertSpeedTo Voltage
Calculate speedsensorvoltage
*** Using function of
*erroramplifier*
CompareSignals
Calculate errorsignal
Fig. 6. A top level behavior of the cruise control system.
IEEE TRANSACTIONS ON SYSTEMS, MAN AND CYBERNETICS, VOL. XX, NO. Y, MONTH 1993
To Calculate:
dutycycleofthrottlecontrolsignal
Provided:
By:
(errorsignal # 0)
makedutycyclebehavior)
Fig. 7. A function MakeT
FISHWICK ET AL.: A MULTIMODEL APPROACH TO REASONING AND SIMULATION
errorsignal # 0
Using function of
* proportional
amplifier*
AmplifySignal
*** Using function of
integralamplifier*
IntegrateSignal
Calculate amplifiederror Calculate errorintegral
*** Using function of
summingamplifier*
Add
Calculate dutycyclecontrolsignal
*** Using function of
*voltagedutycycle
converter*
ControlDutyCycle
Calculate throttlecontrolsignal
Fig. 8. A behavior makedutycycle.
f
IEEE TRANSACTIONS ON SYSTEMS, MAN AND CYBERNETICS, VOL. XX, NO. Y, MONTH 1993
errorsignal # 0
*** by knowledge of
OpAmps
Calculate amplifiederror = Errorsignal *R2/R1
Fig. 9. A low level behavior amplifybehavior.
FISHWICK ET AL.: A MULTIMODEL APPROACH TO REASONING AND SIMULATION
errorsignal > 0
Amplified error = 5 Error integral = 5
Duty cycle control signal =10
DutyCycle of throttle control signal = 0.55
Magnetic force = 0.55
Valve position "Bottom"
Air pressure = 0
Piston position increased by 2
Engine throttle position increased by 2
Vehicle speed = 62
Speed sensor voltage = 62
error signal = 3
Fig. 10. State variables after one "invocation."
IEEE TRANSACTIONS ON SYSTEMS, MAN AND CYBERNETICS, VOL. XX, NO. Y, MONTH 1993
errorsignal > 0
Amplified error = 3 Error integral = 8
Duty cycle control signal =11
DutyCycle of throttle control signal =0.555
Magnetic fo ce =0.555
Valve position "Bottom"
Air press ure = 0
Piston position increased by 2.2
Engine throttle position increased by 2.2
Vehicle speed = 64.2
Speed sensor voltage = 64.2
error signal = 0.8
Fig. 11. State variables after two "invocations."
FISHWICK ET AL.: A MULTIMODEL APPROACH TO REASONING AND SIMULATION
Water
\
0
0
o
0
0
Foam
/
Copper Pot
Heating Element
Fig. 12. A pot of boiling water.
28 IEEE TRANSACTIONS ON SYSTEMS, MAN AND CYBERNETICS, VOL. XX, NO. Y, MONTH 1993
I=ON
not
I=FF Cold Cold I =ONor=0OFF
T=a
.................. .....................
I=ON ..............
from P not Cold

Cold
T=100 (I=OFF and D = Overflow'
Heating
I=ON Boiling Hf = Ht xceptio
'II=N I=0FF
I=IN IO
to Cooling I=ON,
Cold .(I=OFF and
Underflow Overflow
I=ON or IOFF
Fig. 13. Homogeneous FSA refinement.
FISHWICK ET AL.: A MULTIMODEL APPROACH TO REASONING AND SIMULATION
from
Cooling Heating
from
Cold
to
Boiling
to
Cooling
Fig. 14. Decomposition of heating state.
30 IEEE TRANSACTIONS ON SYSTEMS, MAN AND CYBERNETICS, VOL. XX, NO. Y, MONTH 1993
LIST OF TABLES
I Simulation Model Types .................. . ................... ....... 31
II Categorizing Four Approaches ................... ................... ... 32
FISHWICK ET AL.: A MULTIMODEL APPROACH TO REASONING AND SIMULATION
TABLE I
SIMULATION MODEL TYPES
Discrete Space Continuous Space
Discrete Time Discrete Time Discrete Time
Difference Equations Difference Equations
(with integer states) (with real states)
Cellular Automata
Finite State Automata
Continuous Time Discrete Event Continuous
Queuing Models Differential Equations
Digital Logic Models
IEEE TRANSACTIONS ON SYSTEMS, MAN AND CYBERNETICS, VOL. XX, NO. Y, MONTH 1993
TABLE II
CATEGORIZING FOUR APPROACHES
Dynamic Model Geometric Model
Approach State/Event Time Parameter Relation I/O Struc Oper
VSRM symbolic N/A symbolic symbolic symbolic image symbolic
FM real N/A real causal real N/A N/A
QQSIM real real real f. space real N/A N/A
interval real diffeq interval N/A N/A
MI real real real automata real N/A N/A
fuzzy fuzzy diffeq fuzzy N/A N/A
