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

Abstract

We present a KE-tableau-based implementation of a reasoner for a decidable fragment of (stratified) set theory expressing the description logic $\mathcal{DL}\langle \mathsf{4LQS^{R,\!\times}}\rangle(\mathbf{D})$ ($\mathcal{DL}_{\mathbf{D}}^{4,\!\times}$, for short). Our application solves the main TBox and ABox reasoning problems for $\mathcal{DL}_{\mathbf{D}}^{4,\!\times}$. In particular, it solves the consistency problem for $\mathcal{DL}_{\mathbf{D}}^{4,\!\times}$-knowledge bases represented in set-theoretic terms, and a generalization of the \emph{Conjunctive Query Answering} problem in which conjunctive queries with variables of three sorts are admitted. The reasoner, which extends and optimizes a previous prototype for the consistency checking of $\mathcal{DL}_{\mathbf{D}}^{4,\!\times}$-knowledge bases (see \cite{cilc17}), is implemented in \textsf{C++}. It supports $\mathcal{DL}_{\mathbf{D}}^{4,\!\times}$-knowledge bases serialized in the OWL/XML format, and it admits also rules expressed in SWRL (Semantic Web Rule Language).

Figures (9)

• Figure 1: Execution cycle of the reasoner.
• Figure 2: The procedure $\textit{Consistency-}{\undefined{DL}_{\mathbf{D}}^{4,\!\times}}$.
• Figure 3: The procedure $\textit{HOCQA}^\gamma\textit{-}{\undefined{DL}_{\mathbf{D}}^{4,\!\times}}$.
• Figure 4: Expansion rules for the KE$^{\mathbf{\gamma}}$-tableau.
• Figure 5: OWL ontology of the example.