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Extending the Description Logic ALC with More Expressive Cardinality Constraints on Concepts

14 pagesPublished: October 19, 2017


We extend the terminological formalism of the well-known description logic ALC from concept inclusions (CIs) to more general constraints formulated in the quantifier-free fragment of Boolean Algebra with Presburger Arithmetic (QFBAPA). In QFBAPA one can formulate Boolean combinations of inclusion constraints and numerical constraints on the cardinalities of sets.
Our new formalism extends, on the one hand, so-called cardinality restrictions on concepts, which have been introduced two decades ago, and on the other hand the recently introduced statistical knowledge bases. Though considerably more expressive, our formalism has the same complexity (NExpTime) as cardinality restrictions on concepts. We will also introduce a restricted version of our formalism for which the complexity is ExpTime. This yields the until now unknown exact complexity of the consistency problem for statistical knowledge bases.

Keyphrases: cardinality constraints, complexity, Description Logics

In: Christoph Benzmüller, Christine Lisetti and Martin Theobald (editors). GCAI 2017. 3rd Global Conference on Artificial Intelligence, vol 50, pages 6--19

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