# 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} }

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…

## 22 Citations

### On the Expressive Power of Description Logics with Cardinality Constraints on Finite and Infinite Sets

- Computer Science, MathematicsFroCos
- 2019

The main contribution of this paper is to give a characterization of the first-order fragment of \(\mathcal {ALCSCC} ^\infty \), a notion of bisimulation that characterizes this fragment.

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

- Computer ScienceGCAI
- 2017

This work extends the terminological formalism of the well-known description logic ALC to more general constraints expressed in the quantifier-free fragment of Boolean Algebra with Presburger Arithmetic (QFBAPA), and introduces a restricted version of the formalism for which the complexity is ExpTime.

### Expressive cardinality constraints on ALCSCC concepts

- Computer ScienceSAC
- 2019

This work combines the two extensions of description logic ALC by considering extended cardinality constraints on ALCSCC concepts, and shows that this does not increase the complexity of reasoning, which is NExpTime-complete both for extended Cardinality constraints in ALC and A LCSCC.

### On the Complexity and Expressiveness of Description Logics with Counting

- Computer Science
- 2019

This paper investigates the expressive power of the DLs obtained in this way, using appropriate bisimulation characterizations and 0–1 laws as tools to differentiate between the expressiveness of different logics.

### Description Logics That Count, and What They Can and Cannot Count (Extended Abstract)

- Computer ScienceDescription Logics
- 2020

This work extended ALCQ by enabling the statement of restrictions on role successors using the quantifier-free fragment of Boolean Algebra with Presburger Arithmetic (QFBAPA), in which one can express Boolean combinations of set constraints and numerical constraints comparing the cardinalities of finite sets.

### Satisfiability and Query Answering in Description Logics with Global and Local Cardinality Constraints

- Computer ScienceECAI
- 2020

It is proved that decidability of querying can be regained if global and local constraints are not mixed and the global constraints are appropriately restricted, and conjunctive query entailment in this expressive description logic ALCSCC++ turns out to be undecidable.

### Satisfiability Checking and Conjunctive Query Answering in Description Logics with Global and Local Cardinality Constraints

- Computer ScienceDescription Logics
- 2019

It is proved that decidability of querying can be regained if global and local constraints are not mixed and the global constraints are appropriately restricted, and that conjunctive query entailment in this expressive description logic ALCSCC turns out to be undecidable.

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

- Computer ScienceDescription Logic, Theory Combination, and All That
- 2019

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

- Computer Science
- 2019

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.

### Two variable logic with ultimately periodic counting

- MathematicsICALP
- 2020

Decidability issues concerning two-variable logics are reduced to questions about Presburger definability of integer vectors associated with partitioned graphs, where nodes in a partition satisfy certain constraints on their in- and out-degrees.

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