SROIQsigma is decidable
This work addresses a foundational problem in knowledge representation and reasoning, providing a theoretical guarantee for dynamic description logics, though it is incremental in extending existing logics.
The paper tackles the problem of extending the description logic SROIQ with dynamic actions for concept and role changes, proving that the satisfiability problem for this extended logic, called SROIQσ, 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.