• DOI:10.1007/978-3-319-66167-4_3
• Corpus ID: 6705206

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

@inproceedings{Baader2017AND,
  title={A New Description Logic with Set Constraints and Cardinality Constraints on Role Successors},
  author={Franz Baader},
  booktitle={FroCoS},
  year={2017}
}

• F. Baader
• Published in FroCoS 27 September 2017
• Mathematics

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.