The learning step

The Learning Step

The input values of the net, for the learning stage are examples in the outstanding cases, where each premise may be totally realized or not. The net produces its inner representation and hence, generalizes and resolves the intermediate situations. At this level the expressions related to each elementary premise are totally ignored. In fact, it is supposed to be "totally necessary".

Figure 36: A neural network for representation of ((A: very necessary AND B: totally necessary) OR (C: somehow forbidden AND D: totally forbidden))

Table 1: I/O for learning the rule ``if favourable context then (A AND B), O(k)= f(I(A), I(B))'',

I(A)	I(B)	O(K)
1	1	1
1	0	a
1	-1	b
0	0	0
0	1	a
0	-1	c
-1	1	b
-1	0	c
-1	-1	-1

The nets are hierarchical networks of nodes, that contain processing units which perform a memoryless nonlinear transformation on the weighted sum of their inputs.

A node produces a continuous-valued output between -1.0 and 1.0.

Weights are positive or negative real values during training. The output O(k) gives the realization degree of the rule belonging to the interval [+1 -1]:

+1 corresponds to the maximum value of the realization of the rule,
-1 to the minimum value, and
the value 0 corresponds to the case of total uncertainty.

The net uses the backpropagation learning algorithm [RHW92].

For instance , we learn the net such that:

when all the premises of a given rule are realized (i.e. all the corresponding inputs are set to 1), then the output is set to 1 (maximum degree of realization of the concerned rule),
when all the premises are impossible (i.e. all the corresponding inputs are set to -1), the output is set to -1 (minimum degree of realization of the corresponding rule), and
when half of the premises of the rule are realized and the others are not, or no premise at all is realized, then the net learns that the situation is more favourable for the first case than in the second one, and must output values which are relatively great and little for the two respective cases.

Geometrically, the system simulates the behaviour of the function shown figure 37.

Figure 37: Behaviour of the system for the recognition of a rule (A and B are any given proposition).

For a multidimensional system, the net solves the system :

where:

are premises,
are certainty factors and
O(k) is the realization degree of the context defined by the knowledge unit.

When learning "IF favourable context THEN (A and B)", the inputs for the premises C and D are deactivated, and when learning "IF favourable context THEN (C and D)" the inputs for A and B are deactivated.

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