Framework

To enable a uniform framework for all the agents A0, A1 etc. we have to define the main components of such a framework as

1. Environment [E]: An environment as a collection of tasks, which can be solved in this environment.
2. Agents [A]: Some agents, which can be belong to different types.
3. Interface [$\iota$]: The mapping from environmental states into the agent as well as a mapping from agent states to the environment.
4. Experiments [$\mu$]: Defined procedures how one can initialize agents to solve some tasks and to log all important parameters during the behavior sequence.

The agents itself can further be divided, e.g.

1. Agent-Base [AB]: The structure for the agents, which can be scaled to the different types.
2. Agent-System Function [$\gamma$]: The function which defines the overall behavior bound to the structure.

This can be written as follows:

$$EF(x) iff x = \langle E, A, \iota, \mu\rangle$$ (4.2)

$$\iota : E \leftrightarrow A$$ (4.3)

$$\mu : E \times \iota \times A \longmapsto LOG$$ (4.4)

$$A(x) iff x = \langle AB, \gamma\rangle$$ (4.5)

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

$$\iota = (ainp \cup fit) \oplus aout$$ (4.6)

$$ainp : E \times A \longmapsto \Sigma^{*}$$ (4.7)

$$fit : E \times A \longmapsto F$$ (4.8)

$$aout : A \rightarrow \Xi^{*}$$ (4.9)

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