Efficient TBox Reasoning with Value Restrictions using the $\mathcal{FL}_{o}$wer reasoner

• URL: http://arxiv.org/abs/2107.12877v1
• Date: Tue, 27 Jul 2021 15:20:53 GMT
• Title: Efficient TBox Reasoning with Value Restrictions using the $\mathcal{FL}_{o}$wer reasoner
• Authors: Franz Baader, Patrick Koopmann, Friedrich Michel, Anni-Yasmin Turhan, Benjamin Zarrie{\ss}
• Abstract summary: $mathcalFL_o$wer can deal with written in the extension $mathcalFL_bot$ of $mathcalFLFL$ with the top and the bottom concept. $mathcalFL_o$wer can also deal with written in the extension $mathcalFL_bot$ of $mathcalFLFL$ with the top and the bottom concept.
• Score: 8.977167559181982
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The inexpressive Description Logic (DL) $\mathcal{FL}_0$, which has conjunction and value restriction as its only concept constructors, had fallen into disrepute when it turned out that reasoning in $\mathcal{FL}_0$ w.r.t. general TBoxes is ExpTime-complete, i.e., as hard as in the considerably more expressive logic $\mathcal{ALC}$. In this paper, we rehabilitate $\mathcal{FL}_0$ by presenting a dedicated subsumption algorithm for $\mathcal{FL}_0$, which is much simpler than the tableau-based algorithms employed by highly optimized DL reasoners. Our experiments show that the performance of our novel algorithm, as prototypically implemented in our $\mathcal{FL}_o$wer reasoner, compares very well with that of the highly optimized reasoners. $\mathcal{FL}_o$wer can also deal with ontologies written in the extension $\mathcal{FL}_{\bot}$ of $\mathcal{FL}_0$ with the top and the bottom concept by employing a polynomial-time reduction, shown in this paper, which eliminates top and bottom. We also investigate the complexity of reasoning in DLs related to the Horn-fragments of $\mathcal{FL}_0$ and $\mathcal{FL}_{\bot}$.

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