A C++ reasoner for the description logic $\mathcal{DL}_{\mathbf{D}}^{4,\!\times}$ (Extended Version)

Abstract

We present an ongoing implementation of a KE-tableau based reasoner for a decidable fragment of stratified elementary set theory expressing the description logic $\mathcal{DL}\langle \mathsf{4LQS^{R,\!\times}}\rangle(\mathbf{D})$ (shortly $\mathcal{DL}_{\mathbf{D}}^{4,\!\times}$). The reasoner checks the consistency of $\mathcal{DL}_{\mathbf{D}}^{4,\!\times}$-knowledge bases (KBs) represented in set-theoretic terms. It is implemented in \textsf{C++} and supports $\mathcal{DL}_{\mathbf{D}}^{4,\!\times}$-KBs serialized in the OWL/XML format. To the best of our knowledge, this is the first attempt to implement a reasoner for the consistency checking of a description logic represented via a fragment of set theory that can also classify standard OWL ontologies.

Figures (11)

• Figure 1: Execution cycle of the reasoner.
• Figure 2: Expansion rules for the KE-tableau.
• Figure 3: KE-tableau procedure for the saturation of $\undefined{DL}_{\mathbf{D}}^{4,\!\times}$ KBs.
• Figure 4: A simple OWL ontology.
• Figure 5: Internal representation of the $\undefined{KB}$.