General Theory of Exobehaviours: A New Proposal to Unify Behaviors - Foundations on Natural and Artificial Computation - page 25

future state of a system at macroscopic level through mechanical calculations in
the microscopic level due to the number of particles. The order of magnitude of
particles in a macroscopic system is 10 23 .
On the other hand, the microscopic interpretation of fas makes compatible
the idea of a property of the matter which is proposed in the GTE with the
hypothesis which have been used by cognitive psychology and AI in his research
that mind is a computational process.

3.2 The Mathematical Description of Fas

The next question is how to describe the values of the fas. The mathematical
framework to describe the values of the fas must comply with certain require-
ments. The first one is that it must be independent of the computational mech-
anism. The reason for this requirement is that an animal has a neural network,
a bacterium has a biochemical network and a computer has a finite record archi-
tecture, but each of its fas values should be described in the same mathematical
framework. The mathematical framework that satisfies the requirement comes
from the works to explore the limits of computable. Turing found a limit of com-
putable, but the limit found belonged to Turing machines. Thus, it was needed
to know if the Turing limit was the same regardless of the mechanism of com-
putation. For this purpose, a functional approach was applied. Therefore, the
functional approach is the appropriate mathematical framework, and a value of
fas be described using a function. It is important to note that a value of fas, due
to the microscopic interpretation of the fas, can store information which could
change its response to the future. Therefore, the functions are of computational
type. Another important requirement is that the mathematical framework must
reflect each computational operation which is made by a system. Thus, the func-
tions must be intensional[15]. According to this, the general equation of the GTE
is the following functional equation.

ε s ( t )= ρf s ( p 0 , ..., p m ) m 0

≥

ε s ( t ) are the values of the exobehaviour of the system-s in the moment t .
ρ is the relation between fas and the exobehaviour of a system.
f s ( p 0 , ..., p m ) is the function that describe the fas value of the system-s.
p 0 , ..., p m are parameters.

Thus, in the GTE, exobehaviors and fas are related by the above equation. So a
value of fas is described by a function and every function that describes a value
fas has its own parameters.

4 Postulates

Psychology and AI have been investigating in creating theories to predict and
generate behavior, but their investigation ends in achieving predict or generate