  We consider a dynamic extension of the description logic $\mathcal{SROIQ}$.
This means that interpretations could evolve thanks to some actions such as
addition and/or deletion of an element (respectively, a pair of elements) of a
concept (respectively, of a role). The obtained logic is called
$\mathcal{SROIQ}$ with explicit substitutions and is written
$\mathcal{SROIQ^\sigma}$. Substitution is not treated as meta-operation that is
carried out immediately, but the operation of substitution may be delayed, so
that sub-formulae of $\mathcal{SROIQ}^\sigma$ are of the form $\Phi\sigma$,
where $\Phi$ is a $\mathcal{SROIQ}$ formula and $\sigma$ is a substitution
which encodes changes of concepts and roles. In this paper, we particularly
prove that the satisfiability problem of $\mathcal{SROIQ}^\sigma$ is decidable.
