A Formal Environment Model for Multi-Agent Systems - Formal Methods: Foundations and Applications - page 66

through its replication operator. Finally, it has few operators and a simple op-
erational semantics, which is attractive for implementation.
It is worth to note that despite all of these qualities of process algebras in
general, and of π -calculus in particular, they are not usually employed in the
context of multi-agent systems simulation. One exception is the work of Wang
and Wysk [12], which uses a modified π -calculus to express a certain class of
agents and their environments. But their approach is not sucient to deal with
our problems, and thus we develop our own method.
We purposefully treat agents as black-boxes here. This does not mean that
they have no known internal structure; it merely means that such structure is
mostly irrelevant as far as their environment is concerned. We assume, thus, that
those two aspects of a MAS are complementary, but separate, issues. However,
there must be a way to interface the agents with their environment. This is
achieved through the assumption that agents receive stimuli as input and that
they output actions .
The text is organized as follows. Section 2 introduces the basic features of the
model, and also provides their semantics. Section 3, in turn, defines a number of
convenience elements, which are not fundamental, but form a valuable specifica-
tion repertoire. The reader is supposed to be familiar with the π -calculus process
algebra, though the presented specifications are straightforward and should per-
haps be accessible to anyone with some knowledge of process algebras. Section 4
presents a concrete example of an EMMAS specification. At last, Sect. 5 summa-
rizes the main points presented and considers the new perspectives that EMMAS
brings. The present text is based on and an evolution of a longer technical report
[9], which the reader might wish to consult as well.
For the sake of readability, we have omitted π -calculus input and output
parameters when such parameters are not relevant (e.g., we write a instead of
a ( x )

if x is not used later).

2 Environment Model

Our Environment Model for Multi-Agent Systems (EMMAS) is a mathematical
framework that can be used to specify environments for multi-agent systems. Its
translation to the π -calculus process algebra is achieved using a translation func-
tion to map constructs of EMMAS into π -calculus expressions (i.e., a construct
C is translated to

] π ). The full definition of such a function will be given as
new constructs are introduced, and for the moment the following suces.

[ C

Definition 1 (Translation function). The translation function [] π maps

constructs of EMMAS into π -calculus expressions.

2.1 Underlying Elementary π -Calculus Events

A π -calculus specification can be divided into two parts. First, and most funda-
mentally, it is necessary to specify the set of events that are particular to that