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C0041-05.gif is the set of feasible or possible plans of the form C0045-01.gifC0045-02.gif appropriate to the problem being investigated.
e represents the range of possible environments or, equivalently, the initial uncertainty of the adaptive system about its environment. When the plan t tries a structure C0045-03.gif at time t, the particular environment C0021-01.gif confronting the adaptive system signals a response I(t) Î I . The performance or payoff µE(C0031-01.gif), given by the function C0045-10.gif, is generally an important part of the information I(t). Given E ¹ E' for E, C0045-09.gif, the corresponding functions µE, µE' are generally not identical so that a major part of the uncertainty about the environment is just about how well a structure will perform therein. When a plan employs, or receives, only information about payoff so that C0045-11.gif it will be called a payoff-only plan.
Finally, the various plans in C0041-05.gif are to be compared over e according to a criterion C0042-06.gif. Comparisons will often be based on the cumulative payoff functions C0045-05.gif, where C0045-06.gif is the expected payoff under C0040-08.gif(t), and the "target" function C0045-07.gif. An interim behavior criterion, based on a selected sequence C0045-08.gif and of the form
C0045-04.gif
will be important in the sequel.
With the help of this framework each of the fundamental questions about adaptation posed in chapter 1, section 1, can be translated into a formal counterpart:
OriginalFormal
To what parts of its environment is the organism (system, organization) adapting?What is e?
How does the environment act upon the adapting organism (system, organization) ?What is I?
What structures are undergoing adaptation?What is C0021-03.gif?
What are the mechanisms of adaptation?What is W?
What part of the history of its interaction with the environment does the organism (system, organization) retain in addition to that summarized in the structure tested?What is C0039-02.gif ?
What limits are there to the adaptive process?What is C0041-05.gif?
How are different (hypotheses about) adaptive processes to be compared?What is C0042-06.gif?

 
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