Formalization of the Artificial Life Systems

[Vladimir Jojic]

Formalization of the Artificial Life Systems
(very informal)



Artificial Life is based on the idea of the autonomous agent.  Autonomous
agents perceive world around them by sensors and act by effectors, that
way interacting among themselves and the environment in which they exist
etc.  (you know all that ...). 

Sounds ok? But what is the environment, what is the agent, how did we
define them? And did we define them (if anybody knows about formal
definition, tell me)? We have a descriptive definition of the agent and
environment, and that is all. What happens, when we want to bring two
different environments into one? How do we translate different worlds into
each other? How do we group agents, how do those groups interact?  Should
we leave everything to emergent behavior of the groups... 

I am trying to develop a simple formal definition of the artificial life
systems, and some techniques for solving some standard problems by using
the formal approach. 

I will mention some things that I am thinking about ...:

(I am not sure that term *affine* spaces  exists in terminology of
linear algebra in English. I am using Russian text books and there might
be some differences ...)

Representing worlds as an affine n-dimensional space, agents as points,
behavior with vectors in n-dimensional spaces (as introduced by Steels).
Using addition, multiplication (and newly defined operators)  over the
vectors (behavior) to produce emergent behavior (vector). Using
projections and subspaces for grouping agents (or behaviors). Mapping
different worlds onto each other, translating behavior in one world to
behavior in another (do we all perceive things the same way).  Adding time
as an dimension and analysis of these spaces. 

--------------------------

I am not interested in the fact that n-dimensional spaces are hard to
implement and manipulate on the computer (in fact, I do not intend to use
the n-dimensional spaces (stored in matrix or lists), I just want to be
able to use the data in the each agent and in the space as it were just a
part of the n-dimensional space, and manipulate with it).

If I succeed in creating this definition (and it should be rather easy) it
will be a lot easier for me to apply some standard mathematical apparatus
to artificial life systems(and even more importantly, I will be able to
prove that I `have the right' to use it), like things available in
numerical mathematics (multi-grids, for example). 


---------------------------

Send me an e-mail if:  

- you think this won't work and you know why it won't work ...

- you know that this, or anything similar has been done (and have some
proof of that, reference for example) or you are working on it

- you have access to early autonomous agents works (I don't! :( and you
could tell me how they defined it

btw. I am not saying that descriptive definition is not good, actually I
will be using it as the basis for the whole thing (implicitly)


Every advice, suggestion or an answer to a question mentioned above will
be appreciated,

Mr.Vladimir Jojic







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