\gamma_i, \phi_i)$ of an adaptation domain $\mathcal{A} = \{(E_1, \gamma_1, \phi_1), ..., (E_n, \gamma_n, \phi_n)\}$.

#### Test cases the system mastered.

In some cases, adaptive systems may produce innovative behavior before we actively seek it out. In this cases, it is helpful to formalize the produced results once they have been found so that we can ensure that the system’s gained abilities are not lost during further development or adaptation. Formally, this case matches the case for “observed behavior” described above. However, here the test case $(X, Y, g, f)$ already existed as a scenario, so we just need to update $g$ and $f$ (with the new and better values) and possibly $Y$ (if we want to fix the observed behavior).

#### Logical formulae and constraints.

Commonly, constraints can be directly expressed in the adaptation domain. Suppose we build a system against an adaptation domain $\mathcal{A} = \{(E_1, \gamma_1, \phi_1), ..., (E_n, \gamma_n, \phi_n)\}$. We can impose a hard constraint $\zeta$ on the system in this domain by constructing a constrained adaptation domain $\mathcal{A'} = \{(E_1, \gamma_1 \land \zeta, \phi_1), ..., (E_n, \gamma_n \land \zeta, \phi_n)\}$ given that the logic of $\gamma_1, ..., \gamma_n, \zeta$ meaningfully supports an operation like 