I. INTRODUCTION
Why do we use computer simulations? Winsberg in [
1
]
claims that “simulations are often performed to investigate
systems for which data are sparse”. An assumption that
stands behind the use of simulation as a tool to investigate
reality is that reality cannot be known analyzing what can
be considered as its single parts or components, but only by
recreating it from its components. Assertors of the efficacy
of the scientific use of simulation claim that a simulation
expresses a theory, and that a theory expressed by a simulation
produces a series of empiric predictions that can be directly
compared to reality. This consideration lays on the conviction
that a simulation is also a way to build up a scientific
theory as it allows to check immediately the consequences
of our assumptions and gives us precise indications for the
correction or reformulation of a theory. Computer extends
our calculus and memory capacity, and simulations that run
on a computer are considered a method to study complex
systems thanks to the possibility that they give to handle
complex models. Under this extent computer simulations are
also considered as virtual experimental laboratories to study
phenomena that are difficult to observe directly. However
there are also many objections to the use of simulations in
science. Daniel Dennett in [
2
] asks if we can consider real
motion what we see in the Cellular Automata world or if it
is only apparent motion (the consideration can be referred to
Multi-Agent based Simulations as well). Dennett says “The
flashing pixels on the computer screen are a paradigm case,
after all, of what a psychologist would call apparent motion
[...] should we say at least that these moving patterns are
real?”. Dennett, explaining another objection to the use of
Cellular Automata simulation in [
2
] affirms that “There has
been a distinct ontological shift as we move between levels
[...] whereas at the physical level there is no motion, and only
individuals, cells are defined by their fixed spatial location,
at design level we have the motion of persisting objects
[...]”. In fact when a real phenomena is studied by means
of software entities that interact in a computer, it is not easy
to demonstrate the correspondence of the dynamics observed
in the computer to the ones that belong to a real phenomena.
These are not the only objections to the “scientific” use of
simulations. The introduction in a simulation of a certain
amount of arbitrary details (or assumptions), that are not
derived from observations, is often necessary in order to make
the simulation run. This makes then difficult to understand
which outputs of the simulation are really meaningful and
which are instead effects of the introduction of the arbitrary
details that we put into the simulation. Moreover, simulations
are also criticized to be too simplified in respect to reality as
it does not exist a defined criteria to guess if simplifications
operated in building a simulation are the good ones. Other
considerations regard the fact that simulations do not tell
anything new as they are fully deterministic and just give
back as output the same information that we put in input.
Although many of these objections can be directed also to
common scientific practice (more considerations about this
topic can be found summarized in [
3
] [
4
]) it is undeniable that
scientific investigation by simulation is an activity that has to
be performed carefully; in fact the possibility of
misinterpretation of data is higher than in common experimental practice,
exactly due to the “ontological shift” mentioned by Dennett.
Winsberg in [
1
] makes clear that many layers of models are
involved in a simulation and different resources are used in
each inferential step that is presumed in the shift from one
layer to another. Winsberg, again in [
1
], explains that by these
steps the simulation, from an existing theoretical knowledge,
attempts to extract new knowledge about the system being
simulated. This article explores the role of a specific kind of
computer simulations, the MABS, in scientific investigation. In
Section II-A is presented a brief overview of some definition
of model in science and the relation that exists between a
model and a theory. In Section II-B is introduced the scientific
cycle in experimental science, in order to make, in Section III,
a correlation between models in science and models in
simulations. The point of view of the article is that computer
simulations are not only scientific “ models” of phenomena
but are constituted of different layers of abstractions and
present one step more in relation to scientific abstractions
in experimental science. A schema of the abstractions that
are implicitly involved in simulation practice is proposed and,
in Section IV, we suggest that, if this activity is interpreted
under this perspective, an answer can be found to some of
the objections that are often moved to the use of simulation in
scientific investigation. In Section V are stated the conclusions.
II. MODELS AND THEORIES
A. A reflection on Models and Theories
Doran and Gilbert in [
5
] define a model as something that is
similar to a target system T but easier to observe. A model M
of a target system T consist in an entity that becomes the object
of study in place of T in all the cases where this last cannot
be studied or observed directly. Doran and Gilbert explain
that the idea of the possibility of studying a model of T in
place of T is based upon the conviction that if something
is proved to be true in the model then it must be true also
in the target system if, in the design of the model, some
characteristics of the behavior of the target system have been
“ captured” by the model. This definition of model is close to
the one given by Bruce Edmonds in [
6
]. Edmonds defines a
model as something that “ enables an inference process such
that the process enabled in the model corresponds to some
aspects of an observed process” . For this reason the result of
the “ inferential process” in the model, if the initial conditions
are set properly, remarks the author, predicts some aspects of a
subsequent state of the system that is under study. According
to Edmonds’ opinion, in science a natural process is encoded
in a model; the model performs the inference process and
then the results of the inference are decoded and projected
to reality in order to state a prediction. Edmonds in his article
adds that something is a model of “ something else” if the
diagram in Figure 1 “ commutes” and though same results
follow both the lines. Under this perspective the inference
process is thus assigned to the model. Analogously R.I.J.
Huges in [
7
] explains that a model must be analyzed by
three activities of mind that are: denotation, demonstration and
interpretation. In Huges’ opinion, denotation is the “ core” of
the representation and consist in symbols that stand or refer to
parts of the target system; demonstration refers to the internal
dynamics of the representation (the model) whose effects can
be examined; interpretation instead consist in the examination
of the behavior of the model in order to draw conclusions on
the behavior of the world. Eric Winsberg in [
8
] states that as
“ models are partially independent of both theories and the
world [...] they can be used as instruments of exploration
in both domains” . But for this same reason, that a model
is independent both of empirical facts and of theories, the
translation of the model in the target system must be accurately
specified. This independent status of models is remarked also
in many other works found in literature (see [
9
] [
10
]).
We have spoken about the role of models in relation to
theories. But what is then a scientific theory? M.L.Dalla Chiara
and G.Toraldo di Francia in [
11
] explain that a theory is
a form of knowledge that resumes a set of laws that can
be applied to infinite different cases. The authors add that
a form of knowledge has an axiomatic structure and from
that axioms, or initial postulates, by a relation of logical
consequence is established the set of derived propositions that
the theory asserts. This is what is called syntactic definition
of theory, but it does exists also a semantic definition stating
that some kinds of theories are isomorphic to reality and
that the inference steps, bringing from the set of assumptions
to the consequences of the theory, are not deductive (see
Winsberg [
1
]).
From these considerations we can infer that a model in
science derives from a theory, but it is also something that
corresponds to reality, although it is distinct also from it.
That “ correspondence” , to be taken for granted, must be made
explicit although it can be proved only by empirical facts.
B. Model, Theories and Phases in Physics
Experimental science is founded on the concept of
experiment and of observation of phenomena. David Hestenes in [
12
]
asserts that “ the construction of a physical model reduces a real
system to an abstract model that it is possible to translate in
a mathematical form” . Under his perspective a “ mathematical
model is at a higher abstract level and constitutes the highest
abstraction of the knowledge process” (i.e. equations). The
description of the observed phenomena is then constituted by
the analytical or the graphic relations between sizes [
12
]. Axel
Gelfert, in [
13
] states that a mathematical model, in the sense
close to the one meant by Hestenes, is a set of equations,
theorems and definitions but, Gelfert remarks, the equations do
not constitute, by their own, a model of anything (neither of a
class of phenomena) unless an interpretation that connects the
variables with aspects of observable phenomena is established.
We exemplify this process with the schema in Figure 2. In the
same direction is also the definition given by Dalla Chiara and
Toraldo di Francia that in [
11
] claim that a physical model
can be identified with a structure M = <M at; Exp; T ra>
where M at represent the mathematical part, Exp represents
the experimental part, and T ra is a function of translation
that associates a mathematical interpretation to the elements
of the experimental part. Axel Gelfert again in [
13
]
underlines that mathematical models, like other kinds of models,
require background assumptions for their interpretations. This
perspective is not contrary either to what says Huges that in [
7
]
makes clear that physical theories are not statements about
physical world, on the contrary, they are statements about
theoretical constructs and only if the theory is satisfactory then
these constructs stand in a particular relation to the world. In
next section some considerations about MABS and models are
introduced.
The role of the mathematical model in physics is clear, and
it appears to us in tune with the considerations about models
that we saw in the previous paragraph.
III. MODELS AND PHASES OF A SIMULATION
Our interpretation is that Multi-Agent based Simulations
match many of the definitions of model that have been
exposed in the precedent paragraphs. Edmonds in [
6
] states
that MABS attempt to model Multi-Actor Systems with a
Multi-Agent System. The attempt is to investigate a system
by the construction of a MAS model and the analysis of the
behavior of the MAS when it runs. In the opinion of Edmonds
what distinguishes MABS from other forms of modeling is
that simulations based on a Multi-Agent System adopt a MAS
as formal model (in physics that role is of mathematics).
Often in MABS object-actors or other entities of the system
under study (the target system) are mapped onto agents in
the MAS. Edmonds explains that the entities in the real
system correspond to those of the agents in the MAS, while
interactions between entities are correspondent to interactions
rules between agents. Edmonds considers a MABS as a model
of the target system. In his work he does remain at a high level
and suggests interesting epistemological considerations about
the MABS. On the basis of his work we would like to attempt
a step further and try to detail the abstractions that constitute
a MABS. A first consideration is that in a MABS reality is
not directly mapped in a MAS, as one might be induced to
think by looking casually at Edmonds’ diagram, but what that
is mapped it is a model of reality (see Figure 3). This model
is an intermediate step between reality and MAS. Looking
deeper at the different passages implied in the construction
of a simulation model using a MAS, it appears clear that
implicitly we are working also with other intermediate models.
Each model represents a level of abstraction. In fact when we
want to study a phenomenon by a computer simulation a first
theoretical representation has to be translated through many
others steps before it can run on a computer. For this reason
Fig. 3. Edmonds’ schema revisited by the means of the introduction of
another intermediate level.
to use computer simulation to do science, it must be kept a
trace of all the passages that from reality bring to the software
code.
Our proposal is schematized in Figure 4. In the left side
of the schema are shown the existent levels that we identify
between reality and software code. The circularity of the
process of simulation described by Edmonds is maintained
in our proposal. In the right side of the schema in Figure 4,
in fact, are described the necessary steps that have to be
followed to turn back simulation results to reality. In the next
part of the paper we describe in details the meaning and the
importance of each level shown in the schema. Edmonds in
his article identifies also some phases in the simulation process
(Design, Inference, Analysis and Interpretation) and we will
see how they can be mapped in our schema at the end of next
section. Now we will describe in details the meaning and the
importance of each level shown in the schema.
A. Levels of Abstraction in simulation Building
In this section we give a brief explanation of each of
the levels shown in the left side of our schema. The levels
described below have to be considered levels of abstraction
implied (although sometimes implicitly) in MABS. It is not
in the scope of this work to give engineering guidelines
to translate the requirements of a system into the software
implementation, but we want to give a conceptual map of the
structure of the practice of simulation.
1) Target System: this level of abstraction is constituted by
the object of study that is determined by a specific point
of view on a portion of reality, considered “ isolated”
from the rest of the universe. This first abstraction is the
result of the identification of the problem that we want to
examine and it is achieved by the Phase 1 (Observation
in our schema). For example, the target system could
be the urban road system if the goal of the simulation
is to study the urban traffic problem. An example of a
Multi-Agent based traffic model can be found in [
14
].
2) Abstract Model: the second level is the abstract model
of the target system. The model construction (Phase
2) consists in the definition of the elements that are
considered constitutive of the Target System, and in
the formulation of a set of hypothesis (conjectures that
constitute our intuitive theory) about which rules govern
their behaviors and interactions. This definition, at the
beginning, can be also not rigorous. For example, in
the case of the traffic, our abstract model is constituted
by the elements of the environment (i.e. roads,
crossings, traffic lights etc.), the individuals that populates
the environment (cars, motorcycles etc.), the rules of
behavior in this context (vehicles go along the road in
one direction, they stop when the traffic light is red, they
keep a security distance, etc.) and the properties of the
elements that have been identified in that context (each
vehicle has a speed etc.).
3) Computational Model: the third level is the specific
computational model that has been adopted to represent
the abstract model (see Phase 3 in the schema). The
computational model is always a formal model (it can be
a specific MAS). At this level the elements and the rules
described in the precedent level are formally defined
using proprieties and concepts of the MAS model (i.e.
agents, signals etc). In the traffic example cars and traffic
lights can be represented, in a MAS, by different kinds
of agents, while the behavior of the single agents is
modeled giving to the agents the possibility to emit
and interpret specific signals (the red stop lights can be
represented by a signal sent to car that is following).
4) The software model: the fourth level is the software
translation of the Computational Model (Phase 4). The
computational model, as it is, is an abstract definition
and must be translated in a specific program language.
At the end of this 4 steps the original target system will
be completely translated in something that is ready to be
computed by a machine. The translation of that model into
another implies the “ encoding” of a model in the language of
another. This is an activity that is intrinsic to the MABS and it
is strictly related both to scientific activity and to technological
constrains. It is important to be conscious of all these passages
because each translation can introduce errors and sometimes
also a lack of information due to the necessity to use a
less expressive language (e.g. the description of the abstract
model in the language of the MAS model). Therefore, each
abstraction represents another step far from reality because it
implies a transformation of the first model into something else.
For this reason a “ conversion key” that establishes what all the
elements of the various models represents, is needed in order
to maintain a correspondence with reality and use simulation
for scientific investigation.
B. Levels of Decoding
The simulation process proceeds back in the direction of
reality by steps that go through several abstraction levels and
that help to check the effects of the assumptions of the previous
phases and eventually to detect errors or limits of the adopted
frameworks (e.g the selected MAS). Where it is necessary, in
fact, may be necessary to come back to the previous levels and
revise one or more of the models involved in the simulation.
This operation allows also to correct mistakes introduced
in translation phases, and to modify some models by the
introduction of new elements that have been demonstrated
to be necessary in order to obtain meaningful results (see
Figure 5). The four decoding steps are presented below:
1) Output: outputs are the simple results of the software
execution (Phase 5). If some errors are detected in this
step it is necessary go back to the software code.
2) Simulation Displaying: the envisioning of the outputs
(Phase 6) is often the only way to operate with the
simulation dynamic data, because simple outputs are usable
only at a machine level. This step is not trivial because
consists in the representation of real entities by objects
that do not necessarily offer a realistic visualization of
the phenomena. The aim of Simulation Displaying in
fact is to give an immediate and readable interpretation
of the Outputs. This passage is often another abstraction
jump that needs a translation key. The importance of the
visualization of simulation output data has been largely
discussed in many articles (i.e. see Batty and Smith
in [
15
]). This step is very important, in particular for
MAS-based simulations of complex systems, because
the direct observation of the dynamics envisioned, allows
to detect unexpected behaviors. These anomalies will be
resolved in the next steps, and they could induce to a
revision of the software, of the MAS, or the of Abstract
Model. If we focus on the MAS-based traffic model
example, at this level we can observe on the screen the
dynamic evolution of the simulation constituted by the
virtual cars that go along the roads.
3) Theory: after the visualization, the correctness of the
simulation displaying data must “ verified” (Phase 7);
in other words it is necessary to check if our initial
assumptions at the abstract level are captured by the
simulation. This phase is not aimed at evaluating if
the assumptions of the theory are correct, but only at
verifying if these assumptions are maintained in the
simulation. During this phase, we may need to go back
to the software or to the MAS to correct mistakes
and revise our computational modeling choices if we
have some bad feedbacks from the displaying of the
simulation. To turn back to traffic example, thanks to
visualization phase we can observe the cars that move,
brake, form a queue and so on. For example we could
notice an anomalous behavior near crosses because cars
do not give way correctly as we have assumed in our
theory. Therefore we must go back to software in order
to check if we did mistakes in the implementation or
we may be forced to check if we have wrongly mapped
the rules of the Abstract Model in the language of the
computational model.
4) Real Data: after the verification phase next step is
validation phase (Phase 8). If in the previous step we
have decided that our theory is well represented by the
simulation, now we can validate the theory in relation
to real data collected in the target system. In this phase
the results of the simulation must be related to real and
measurable aspects of reality. In a study on the traffic
problem, for example, a portion of a real street must
be simulated and the verified results must be compared
to the real data collected by observations of reality. If
after this check simulation results are considered not
reliable, it is necessary to turn back to the Abstract
Model and change some of the initial assumptions, or it
may be decided the introduction of new elements that at
first time were wrongly considered not relevant for the
representation of the Target System. The not realistic
formation of very long queues, for example, could be
resolved with a revision of the interaction rules between
the cars and by the introduction of the possibility to
overtake when the road on the other way is free.
If the theory is validated by available data then it is possible
to make predictions for future states of the Target System
(Phase 9).
In reference to the work of Edmonds [
6
] the phases of
the simulation process are identified as Design, Inference,
Analysis and Interpretation. These phases in our schema are
visible in Figure 6. The phase of Design in our schema
involves all the 4 abstractions, as to say the Target System, the
Abstract Model, the Computational Model and the Software.
The Inference phase of Edmonds belongs to the level of the
Software abstraction of our schema, the phase of Analysis
involves from the level of Displaying to Real Data, while
Interpretation regards Simulation Displaying and the Theory.
IV. SOME RESULTS FOR THE SIMULATION PRACTICE
In this section the introduction of an example will clarify our
considerations about the aid that the conceptualization given in
the proposed schema can give to simulation activity. Therefore
we will now introduce the work described in [
16
]. In particular
Balmer and Nagel describe a MAS simulation focused on
traffic roundabouts which is applied to a specific Zurich area.
During the phase of Design the authors decided to represent
cars as particles that move along tunnels (driving routes)
representing streets. The spatial model is continuous (the
position of each particle is determined by a pair of coordinates)
and the particles can be considered agents because they have
specific behavior rule (agents must respect the physical rules
of acceleration, they have a specific desired speed, they must
respect other agents in the system decelerating or overtaking
if a slower agent drive in front of them, etc.). Agents also
hold information about their destination. Therefore the target
system is also in this case the traffic dynamics, the abstract
model is constituted by the assumptions and rules like the
ones presented above, while the chosen computational model
is constituted by a set of physical equations describing the
particles motion. During what we have called “ the analysis” ,
in particular in the phase that in our schema is identified with
the number 8 (validation), a problem was detected: in some
situation the cars were subjected to forces exerted in opposite
direction (the forces implied were the one directed towards the
desired way and the repulsion force aimed at the avoidance of
collisions with other cars) and they became unable to move.
This problem could not be identified in the design process
because it can be considered as an emergent phenomenon that
occurs only in some situations and in some specific spatial
contexts. This event is a relevant simulation result, because it
can be a hint of a possible congestion. In this framework it is
then useful to record it, but since this is not a routinary event,
the behavior of agent drivers in this situation cannot modelled
in a simple way. The decision in this case could have been
to turn back to the abstract model and operate a change (i.e.
discretization of space or the introduction of giving way rules).
However Balmer and Nigel anyway decided not to operate
these big changes of their abstract model, but they opted for a
minor modification: the introduction of a compenetration rule
in order to force the cars to go beyond the stall situation and
avoid the deadlock. This is an abstract and gross representation
of a set of complex behaviors that can be assumed by human
drivers to solve a stall. Thanks to this solution the global
behavior of the cars (in sense of aggregate data) maintains
a better similarity with the observed reality. In our opinion
Balmer and Nigel could detect the problem and adopt a good
solution for a correct and scientific use of simulation because
they were aware of all the steps done in the previous design
phase. It is fundamental to be aware of all these passages as
it would be an error to map directly the real world in the
software code. if we follow strictly all the passages shown in
the schema, it is possible to keep track of the translations of
our initial assumptions and, in this way, we can easily avoid
the introduction of arbitrary details whose influence cannot be
kept under control, as pointed out by some of the critics to
simulation practice that we summarized in Section I.
We then suggested that simulations can be used as a valid
tools for scientific investigation as the cycle of a simulation
reflects the cycle of a science like physics, although a further
abstraction is involved in simulation as it is shown in Figure 7.
If we come back to reality following the proposed schema in
all its passages it is possible to obtain meaningful results that
are connected with reality, especially if the revision phases
are performed accurately. This practice is analogous to the
one followed by a science like physics where a first phase of
simplification and abstraction (in newtonian physics reality is
so simplified that bodies are seen just as simple points without
extension, see [
12
]) follows an experimental phase by which
the results obtained in the simplified model are projected back
to reality. These considerations can help to give an answer to
other of the objections presented at the beginning of the paper.
V. CONCLUSIONS
In this paper we began reporting some definitions of what
can be considered a model in science and we briefly described
the scientific cycle in physics. Then we raised some questions
about MABS and their role in scientific investigation. We
started from the work of Edmonds to introduce our
investigation in the nature of simulations in the attempt to give
some answers. Our conclusion is that simulations are not
“ models” but are a compound of many models at different
levels of abstractions. We pointed out that in the encoding or
decoding of one level into another is situated the risk to loose
the scientific purpose of simulations, if a translation criteria
between models is not stated explicitly. When one modeler is
led to revise his/her theory about the simulated domain after an
analysis of simulation results and their validation, simulation
can be considered a useful tool for scientific investigation.
On the other hand, if the simulation has been deeply tested
and we can trust simulation results, we focus on the phase of
simulation prediction. In this last case we are working with a
tested instrument and we are not using MABS to do scientific
investigation but simply, for example, to help decision makers.
It must be noted that other areas of Computer Science and
engineering deal with models and abstractions of real systems,
in particular Software Engineering. For example the problem
of correspondence between models is considered also by the
Model Driven Architecture Approach (MDA), that focuses on
the importance of the mapping between the models present
at different levels of Software Engineering practice. One of
the purpose of MDA is to give guidelines for integration of
Information Technologies in order to assure interoperability
between systems (for an introduction and first references on
MDA see for example [
17
]). Another meaningful example is
the work of M. Jackson [
18
] that analyzes under the
perspective of Problem Frames (PF) the relation that, in Software
Engineering, exists between the requirements, the real world,
and the machine considered as the general purpose computer
that will execute the software. MABS share several aspects
with Software Engineering, because the proposed schema
reminds several iterative software development processes that
are used also to project and build an effective simulation
tool. MDA or PF definitions take in consideration a class
of problems that is involved also in MABS, but our study
does not take into consideration deeply the technical problems
that are strictly related to the machine, the software and the
specific available technologies. The aim of this work is in fact
to state some general considerations that could help to preserve
scientific contents through the many models involved in MAS
simulation practice.