No subject


Mon Jun 5 16:42:55 EDT 2006


A level is composed of a "MEDIUM that is to be processed, COMPONENTS
that provide primitive processing, LAWS OF COMPOSITION that permit
components to be assembled into SYSTEMS, and LAWS OF BEHAVIOR that
determine how system behavior depends on the component behavior and the
structure of the system".

Through the word "level" appears intuitively notion of an entity with
some AUTONOMY, the fact that there are several such entities, 
and RELATIONS (hierarchy), composition laws between them.
Through the word "organization" (within a level), appears the notion of
REGULARITIES, laws (of behavior), within a level.

2.2 Sketch of a formal description :

*****************************************************************
Let us consider :
- a set S1; a relation R1 on S1, both making up structure:<S1,R1>
- a set S2; disjoint of S1, a relation R2 on S2, both making up 
structure:<S2,R2>
- a bijective function f from S1**n (S1xS1x...xS1) to S2,n>1
then I suggest to say that :
[<S1,R1>,<S2,R2>,f] represents an (atomic) organization hierarchy
iff from R2 relation on S2, through f-1 (f inverse function), 
it is not possible to infer a relation R1' on S1.
*****************************************************************

For instance if we consider instruction and bit levels of a computer,
from (logic) relation between two successive instructions, it is not 
possible to infer a relation between bits corresponding to these 
instructions. 
Or in language domain, from (syntactic or semantic) relation between words, 
it is not possible to infer a relation between letters which make up
these words.

This definition does not take in account any environment of the object 
or phenomenon. Only the major notions mentionned above : 
- regularities: relations R1, R2;
- composition law between levels: f;
- autonomy: no R1' relation.
have been considered.
Can such a definition be a (syntactic) bootstrap of a formal description
of organization levels ? 



More information about the Connectionists mailing list