Theoretical Framework

To implement the theoretical concept of the Wilson-Learning Classifier System zcs within our experimental framework , we have to translate his paper into this framework. For this we have to repeat here the basic assumptions for our framework as follows:

$\displaystyle EF(x)$	$\displaystyle iff$	$\displaystyle x = \langle E, A, \iota, \mu\rangle$	(4.43)
$\displaystyle \iota$	$\displaystyle :$	$\displaystyle E \leftrightarrow A$	(4.44)
$\displaystyle \mu$	$\displaystyle :$	$\displaystyle E \times \iota \times A \longmapsto LOG$	(4.45)
$\displaystyle A(x)$	$\displaystyle iff$	$\displaystyle x = \langle AB, \gamma\rangle$	(4.46)

with as a set of values indicating some performances. Within the interface one can assume as a general principle, that there is a mapping from the environment to the agent as one mapping and a mapping from the agent to the environment . Furthermore one can distinguish usual input from a more abstract input called 'fitness function'.

$\displaystyle \iota$	$\displaystyle =$	$\displaystyle (ainp \cup fit) \oplus aout$	(4.47)
$\displaystyle ainp$	$\displaystyle :$	$\displaystyle E \times A \longmapsto \Sigma^{*}$	(4.48)
$\displaystyle fit$	$\displaystyle :$	$\displaystyle E \times A \longmapsto F$	(4.49)
$\displaystyle aout$	$\displaystyle :$	$\displaystyle A \rightarrow \Xi^{*}$	(4.50)

$\Sigma$ as well as $\Xi$ are special alphabets to encode input or output messages. 'F' is a set of fitness values.

Gerd Doeben-Henisch 2012-03-31