SROIQsigma is decidable

TL;DR

This paper introduces a dynamic extension of the description logic SROIQ, called SROIQ^σ, which allows for evolving interpretations through delayed substitutions, and proves its satisfiability problem is decidable.

Contribution

It defines SROIQ^σ with delayed substitutions and proves the decidability of its satisfiability problem, extending the capabilities of description logic reasoning.

Findings

Satisfiability of SROIQ^σ is decidable.

Introduces delayed substitution mechanism in description logic.

Extends SROIQ with dynamic, evolving interpretations.

Abstract

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.