Presburger Concept Cardinality Constraints in Very Expressive Description Logics – Allegro sexagenarioso ma non ritardando

Sebastian RudolphSebastian Rudolph

ISBN: 978-3-030-22101-0
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Sebastian Rudolph
Presburger Concept Cardinality Constraints in Very Expressive Description Logics – Allegro sexagenarioso ma non ritardando
In Carsten Lutz, Uli Sattler, Cesare Tinelli, Anni-Yasmin Turhan, Frank Wolter, eds., Description Logic, Theory Combination, and All That - Essays Dedicated to Franz Baader on the Occasion of His 60th Birthday, volume 11560 of LNCS, 542-561. Springer, 2019

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KurzfassungAbstract
Quantitative information plays an increasingly important role in knowledge representation. To this end, many formalisms have been proposed that enrich traditional KR formalisms by counting and some sort of arithmetics. Baader and Ecke (2017) propose an extension of the description logic ALC by axioms which express correspondences between the cardinalities of concepts by means of Presburger arithmetics. This paper extends their results, enhancing the expressivity of the underlying logic as well as the constraints while preserving complexities. It also widens the scope of investigation from finite models to the classical semantics where infinite models are allowed. We also provide first results on query entailment in such logics. As opposed to prior work, our results are established by polynomially encoding the cardinality constraints in the underlying logic.
Projekt:Project: DeciGUT
Forschungsgruppe:Research Group: Computational LogicComputational Logic

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-030-22102-7_25.

@incollection{R2019,
  author    = {Sebastian Rudolph},
  title     = {Presburger Concept Cardinality Constraints in Very Expressive
               Description Logics {\textendash} Allegro sexagenarioso ma non
               ritardando},
  editor    = {Carsten Lutz and Uli Sattler and Cesare Tinelli and Anni-Yasmin
               Turhan and Frank Wolter},
  booktitle = {Description Logic, Theory Combination, and All That - Essays
               Dedicated to Franz Baader on the Occasion of His 60th Birthday},
  series    = {LNCS},
  volume    = {11560},
  publisher = {Springer},
  year      = {2019},
  pages     = {542-561},
  doi       = {10.1007/978-3-030-22102-7_25}
}