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Efficient TBox Reasoning with Value Restrictions using the ${\cal F}{{\cal L}_0}$wer Reasoner

Published online by Cambridge University Press:  15 October 2021

FRANZ BAADER,
PATRICK KOOPMANNOpen the ORCID record for PATRICK KOOPMANN[Opens in a new window],
FRIEDRICH MICHEL,
ANNI-YASMIN TURHANOpen the ORCID record for ANNI-YASMIN TURHAN[Opens in a new window] and
BENJAMIN ZARRIESS
FRANZ BAADER
Affiliation:
Technische Universitat Dresden, Dresden, Germany (e-mails: franz.baader@tu-dresden.de, patrick.koopmann@tu-dresden.de, friedrich.michel@tu-dresden.de, anni-yasmin.turhan@tu-dresden.de, benjamin.zarriess@tu-dresden.de)
PATRICK KOOPMANN
Affiliation:
Technische Universitat Dresden, Dresden, Germany (e-mails: franz.baader@tu-dresden.de, patrick.koopmann@tu-dresden.de, friedrich.michel@tu-dresden.de, anni-yasmin.turhan@tu-dresden.de, benjamin.zarriess@tu-dresden.de)
FRIEDRICH MICHEL
Affiliation:
Technische Universitat Dresden, Dresden, Germany (e-mails: franz.baader@tu-dresden.de, patrick.koopmann@tu-dresden.de, friedrich.michel@tu-dresden.de, anni-yasmin.turhan@tu-dresden.de, benjamin.zarriess@tu-dresden.de)
ANNI-YASMIN TURHAN
Affiliation:
Technische Universitat Dresden, Dresden, Germany (e-mails: franz.baader@tu-dresden.de, patrick.koopmann@tu-dresden.de, friedrich.michel@tu-dresden.de, anni-yasmin.turhan@tu-dresden.de, benjamin.zarriess@tu-dresden.de)
BENJAMIN ZARRIESS
Affiliation:
Technische Universitat Dresden, Dresden, Germany (e-mails: franz.baader@tu-dresden.de, patrick.koopmann@tu-dresden.de, friedrich.michel@tu-dresden.de, anni-yasmin.turhan@tu-dresden.de, benjamin.zarriess@tu-dresden.de)
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Abstract

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The inexpressive Description Logic (DL) ${\cal F}{{\cal L}_0}$, which has conjunction and value restriction as its only concept constructors, had fallen into disrepute when it turned out that reasoning in ${\cal F}{{\cal L}_0}$ w.r.t. general TBoxes is ExpTime-complete, that is, as hard as in the considerably more expressive logic ${\cal A}{\cal L}{\cal C}$. In this paper, we rehabilitate ${\cal F}{{\cal L}_0}$ by presenting a dedicated subsumption algorithm for ${\cal F}{{\cal L}_0}$, 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 ${\cal F}{{\cal L}_0}$wer reasoner, compares very well with that of the highly optimized reasoners. ${\cal F}{{\cal L}_0}$wer can also deal with ontologies written in the extension ${\cal F}{{\cal L}_ \bot }$ of ${\cal F}{{\cal L}_0}$ 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 ${\cal F}{{\cal L}_0}$ and ${\cal F}{{\cal L}_ \bot }$.

Keywords

description logicsreasoningsubsumption

Information

Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 22 , Issue 2: Special Issue on the International Joint Conference on Rules and Reasoning, RuleML+RR 2019 , March 2022, pp. 162 - 192
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Footnotes

*

This paper is under consideration in Theory and Practice of Logic Programming (TPLP).

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