and its environment $E$, both being modeled as systems again.

Hiding some of the complexity described in [@holzl2011towards], we assume we have a logic $\mathfrak{L}$ in which we can express a system goal $\gamma$. We can always decide if $\gamma$ holds for a given system, in which case we write $S \models \gamma$ for $\gamma(S) = \top$. Based on [@holzl2011towards], we can use this concept to define an adaptation domain:

\[def:adaptation-domain\] Let $S$ be a system. Let $\mathcal{E}$ be a set of environments that can be combined with $S$ using a combination operator $\otimes$. Let $\Gamma$ be a set of goals. An *adaptation domain* $\mathcal{A}$ is a set $\mathcal{A} \subseteq \mathcal{E} \times \Gamma$. $S$ can adapt to $\mathcal{A}$, written $S \Vdash \mathcal{A}$ iff for all $(E, \gamma) \in \mathcal{A}$ it holds that $S \otimes E \models \gamma$.

\[def:adaptation-space\] Let $\mathcal{E}$ be a set of environments that can be combined with $S$ using a combination operator $\otimes$. Let $\Gamma$ be set of goals. An *adaptation space* $\mathfrak{A}$ is a set $\mathfrak{A} \subseteq \mathfrak{P}(\mathcal{E}, \Gamma)$.

We can now use the notion of an adaptation space to define a preorder on the adaptivity of any two systems.

\[def:adaptation\] Given two systems $S$ and 