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Scenarios and scenario models
As formalised by Keppens and Shen [20], a
compositional modeller takes two inputs and produces one output. The
first input is a representation (which is itself a model) that
describes the system of interest by means of an accessible formalism.
This model, which normally consists of (mainly) realworld
participants and their interrelationships, is called the
scenario. The second input is the task description. It
is a formal description of the criteria by which the adequacy of the
output is evaluated. The output is a new model that describes the
scenario in a more detailed formalism, usually a set of variables and
equations, which the modelbased reasoner can employ readily. Such a
model, which normally contains conceptual participants and
interrelationships, is called a scenario model. The aim of any
compositional modeller is to translate the scenario into a scenario
model, by means of the task description.
In this work, a model is formally defined by a tuple
, where is a set of participants and is a set of
relations over the participants in . This definition applies to
both the scenario and the scenario model. A typical example of a
scenario is a description of a predator population, a prey population
and a predation relation between the predator and the prey. This
scenario is a model
with:
Figure 3:
Stock flow diagram of predator prey
scenario model

Table 1:
Variables in the stock flow diagram and the mathematical
model
Symbol 
Variable name 
,

number of predators, prey 
,

natality of predators,
prey 
,

mortality of predators,
prey 

predation of prey 
,

natalityrate of predators,
prey 
,

mortalityrate of predators,
prey 
,

capacity of predators,
prey 

searchrate 

preyhandlingtime 

preyrequirement 

The aim of the compositional model repository is to translate a
scenario into a scenario model. Within this work, both systems
dynamics stockflow formalism [12] and ordinary
differential equations (ODEs) will be employed as the modelling
formalisms. For example, a scenario model that corresponds to the
above scenario is depicted in Figure
3. Formally, a scenario model is
another model
and in this case
The relation between the variables of the mathematical model and those
used in the stockflow diagram is given in table
1. Generally speaking, stockflow
diagrams are graphical representations of systems of (ordinary or
qualitative) differential equations. In the automated modelling
literature in general, and engineering and physical systems modelling
in particular, more sophisticated representational formalisms have
been developed to enable the identification of mathematical models of
the behaviour of dynamic systems from observations. Examples include
bond graphs [17] and generalised
physical networks [9]. However, the potential
benefits of these more advanced formalisms are not exploited here, but
remain as an interesting future work. Instead, stockflow diagrams
are employed throughout this paper as they are far more commonly used
in ecological modelling [11].
It is often possible to construct multiple scenario models from a
single given scenario, and the task specification is employed to
guide the search for the most appropriate one(s). In this work,
scenario models are selected on the basis of hard constraints and user
preferences. The hard constraints stem from restrictions imposed on
compositionality by the representational framework (see section
3.2.3) and from properties the scenario
model is required to satisfy (see section
3.2.3). The user preferences express the
user's subjective view as to which modelling approaches are more
appropriate in the context of the current scenario (see section
2.2).
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Previous: Preliminary concepts
Jeroen Keppens
20040301