A New Description Logic with Set Constraints and Cardinality Constraints on Role Successors

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10483)


We introduce a new description logic that extends the well-known logic \(\mathcal {A}\mathcal {L}\mathcal {C}\mathcal {Q}\) by allowing the statement of constraints on role successors that are more general than the qualified number restrictions of \(\mathcal {A}\mathcal {L}\mathcal {C}\mathcal {Q}\). To formulate these constraints, we use the quantifier-free fragment of Boolean Algebra with Presburger Arithmetic (QFBAPA), in which one can express Boolean combinations of set constraints and numerical constraints on the cardinalities of sets. Though our new logic is considerably more expressive than \(\mathcal {A}\mathcal {L}\mathcal {C}\mathcal {Q}\), we are able to show that the complexity of reasoning in it is the same as in \(\mathcal {A}\mathcal {L}\mathcal {C}\mathcal {Q}\), both without and with TBoxes.



The author thanks Viktor Kuncak for helpful discussions regarding the proof of Lemma 3.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Theoretical Computer ScienceTU DresdenDresdenGermany

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