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SROIQsigma is decidable

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 $\mathcal{SROIQ^σ}$. 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 $\mathcal{SROIQ}^σ$ are of the form $Φσ$, where $Φ$ is a $\mathcal{SROIQ}$ formula and $σ$ is a substitution which encodes changes of concepts and roles. In this paper, we particularly prove that the satisfiability problem of $\mathcal{SROIQ}^σ$ is decidable.