|
|
|
|
|
|
|
can transmit. That is, given a particular signal  at time t, the ith component Ii(t) is the value di(t)of the ith sensor at time t. In general the sets Ii may be quite different, corresponding to different kinds of sensors or sensory modalities. |
|
|
|
|
|
|
|
|
The formal presentation of an adaptive plan t can be simplified by requiring that  serve as the state of the plan at time t. That is, in addition to being the structure tried at time t, must summarize whatever accumulated information is to be available to t. We have just provided that the total information received by t up to time t is given by the sequence  . Generally only part of this information is retained. To provide for the representation of the retained information we can make use of the latitude in specifying  . Think of as consisting of two components  and  , where  is the structure tested against the environment at time t, and the memory  represents other retained parts of the input history . Then the plan can be represented by the two-argument function |
|
|
|
|
|
|
|
|
Here the structure to be tried at time t + 1,  , along with the updated memory  , is given by |
|
|
|
|
|
|
|
|
(The projection of t on , |
|
|
|
|
|
|
|
|
is that part of t which determines how the plan's memory is updated.) It is clear that any theorems or interpretations established for the simple form |
|
|
|
|
|
|
|
|
can at once be elaborated, without loss of generality or range of application, to the form |
|
|
|
|
|
|
|
|
Thus the framework can be developed in terms of the simple, two-argument form of t, elaborating it whenever we wish to study the mechanisms of trial selection or memory update in greater detail. |
|
|
|
|
|
