013-Some Symbolic expression of objects and representations

Symbolic expressions of objects, their relation and representation - Models for expressions of a theory of representation:

Here are basic examples of representational combinations, with the function of awareness this forms a basis for a symbolic theory of representation:

Any object X is identical to itself.
X = X

Some object X is not identical to another object Y.
X != Y 

An object may be a set.  Definition of a set: A set is an object which is identical to a group of objects. Some object Q which is objects X,Y,Z.
Q = (X,Y,Z)  This is an arbitrary association.

An object X is identical to itself if it is X of set.
X = X:(X, Y, Z)

An object X is identical to itself if it is X of set Q.
X = X:Q

An object X representing another object Y is a relationship of objects X and Y; this relationship is a representation.  

The group of objects which is "X representing Y is an object" is the same as X representing Y.
(X;Y) = X;Y

The group of objects which is "X representing Y" is an object itself that can be expressed as a set.
(X;Y) = set N

Any object X is identical to itself representing itself (object self-representation).
X = X;X

Object X representing object Y is the same as object Y representing object X; where objects X and Y have the same relationship. eg.  Monster as little girl = little girl as monster.

X;Y = Y;X

Any object X is itself representing another object Y.
X = X;Y

An object X is equivalent to, or the same as another object which is the set "X as Y"
X = (X;Y)

X is equivalent to the set object, "X representing Y" or the set object "X representing Z".
(X;Y) = X = (X;Z)

X is the same as X, representing Y.  And the same as X, representing Z.
Y;X = X = X;Z

There are three kinds of sets: Simple sets, associative sets, and representational sets. A simple set is a group of objects. 

A simple set is Q where Q = (a,b,c)

An associative set is is a group of objects where the objects of the set have a representational relationship with one another

Set M where M = (A,B,C) and where A = A;m, B = B;m, C = C;m  
A set M whose objects are associated to some object m
A is A:(A, B, C) or A:M or A as an element of M --> A as an instance of m -> A;m
: indicates "of"  where an object is an element of a group.  What forms this group is the association to m.  (see connecting and disconnecting - representation making)

A representational set is a set N where N = (X;Y)

The set of X representing Y is not identical to the set of X representing Z; because the objects of each group are not the same.
N = (X;Y) ≠ (X;Z) = M
N ≠ M

X = X;Y and Y = Y;X, but X ≠ Y. X is representationally connected to Y. X;Y is not an object (the set N) in this equation; it is a relationship of objects X and Y. X and Y have the same relationship to one another; this relationship is a representation Thus they are representationally connected.  If we think of X;Y as an object itself, that is another representation that is distinct from the association or connection of X;Y.  Thus (X;Y) = X;Y, but the set (X;Y) is different from X;Y because it is a thing itself not merely a connection or association or relation.  When X;Y form a set, we can represent them as a separate object such as N.

Objects, sets, associative sets, representational sets should give us the explanatory power to describe the contents of awareness.  Hopefully, these should be sufficient to describe and develop the mechanism for how complex associations will be made by our AI.  

example set structures of representation:
                X = X;Y
                N = N;(X;Y)
                M = M;(X, X, X)
                Q = Q;((X;Y), (X;Z), (X;T))
                X = X:(X, Y, Z)
                X = X; X:(X,Y,Z)
                X = X; X:(X;Y)

Identity expressions can be replaced by flow expressions.  where X -> X;Y -> Y

identity and flow are both expressions of a relationship.  We can replace identity or flow expressions with representations directly.  Thus X; (X;Y)   

or  (X ; (X;Y) ; Y)
 (X ; (X;Y) )
     ( (X;Y) ; Y) 

These kinds of structures that we show symbolically, we make in our experience.  That is, the symbolic expression stands in for the kind of experience to let us do more sophisticated modeling. 

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