formal definitions of our vocabulary related to the description of systems from [@holzl2011towards]: We describe a system as an arbitrary relation over a set of variables.

\[def:system\] Let $I$ be a (finite or infinite) set, and let $\mathcal{V} = (V_i)_{i \in I}$ be a family of sets. A *system* of type $\mathcal{V}$ is a relation $S$ of type $\mathcal{V}$.

Given a System $S$, an element $s \in S$ is called the state of the system. For practical purposes, we usually want to discern various parts of a system’s state space. For this reason, parts of the system relation of type $\mathcal{V}$ given by an index set $J \subseteq I$, i.e., $(V_j)_{j \in J}$, may be considered *inputs* and other parts given by a different index set may be considered *outputs* [@holzl2011towards]. Formally, this makes no difference to the system. Semantically, we usually compute the output parts of the system using the input parts.

We introduce two more designated sub-spaces of the system relation: *situation* and *behavior*. These notions correspond roughly to the intended meaning of inputs and outputs mentioned before. The situation is the part of the system state space that fully encapsulates all information the system has about its 