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The application of decomposition based on the Cartesian product gives two pos-
sibilities: it can be used in the category of algorithms and in the category of sets
and mapping.
The use of the concept of the Cartesian product in the category of algorithms makes
it possible to receive autonomous component algorithms, which are independed,
but this process of decomposition is difficult and not always possible in practice.
The application of the concept of the Cartesian product in the category of a set
and mapping is easier in practical applications, but it usually does not result in
autonomous partial algorithms. However, it is possible to regain (at least to some
certain extent) this autonomy.
One method of gaining autonomy is the application of the communication process
between the partial algorithms. It leads us to the concept of an object.
The other method of gaining autonomy is the use of operation of observation of
the environment (including other agents) which makes it possible to formulate the
concept of an agent . It is noteworthy that this observation may be used for some
kind of communication between agents, so that one agent makes a certain change
of the chosen attribute of environment (or a characteristic modification of the state
of the environment), and the other agent observes this change and interprets it.
The aim of the considerations was to define such notions as decomposition and
autonomy, which resulted in defining an agent as an autonomous (to a certain extent)
algorithm (program) equipped with the capability to communicate and cooperate
whose distinguishing feature is the capability to observe the environment in order to
recognize actions undertaken by other agents existing in this environment.
The formulations we obtained may be used for defining agents operating in
computer systems as well as for constructing agent systems, oriented towards
defined areas of applications, which will be presented later in further chapters
(Chaps. 3 and 4 ) .
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