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… 
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Presburger Concept Cardinality Constraints in Very Expressive Description Logics - Allegro sexagenarioso ma non ritardando
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TLDR
The proposed extension of the description logic by axioms which express correspondences between the cardinalities of concepts by means of Presburger arithmetics is extended, enhancing the expressivity of the underlying logic as well as the constraints while preserving complexities.
Integrating Reasoning Services for Description Logics with Cardinality Constraints with Numerical Optimization Techniques
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Well-established techniques from the eld of numerical optimization, such as column generation, in order to obtain more practical algorithms are used for dealing with counting quanti ers over unary predicates based on SAT-based column generation.
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We introduce a new description logic that extends the well-known logic ALCQ by allowing the statement of constraints on role successors that are more general than the qualified number restrictions of
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