Attributive concept descriptions with complements
Artificial Intelligence
Editorial: Knowledge Representation and Reasoning in Software Engineering
IEEE Transactions on Software Engineering - Special issue on knowledge representation and reasoning in software development
On the relative expressiveness of description logics and predicate logics
Artificial Intelligence
The complexity of concept languages
Information and Computation
Description logics for conceptual data modeling
Logics for databases and information systems
Description Logics: Foundations for Class-based Knowledge Representation
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
Reasoning in expressive description logics
Handbook of automated reasoning
Complexity of Two-Variable Logic with Counting
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Two-variable logic with counting is decidable
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
The description logic handbook: theory, implementation, and applications
The description logic handbook: theory, implementation, and applications
Ontology reasoning in the SHOQ(D) description logic
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Relationships between nondeterministic and deterministic tape complexities
Journal of Computer and System Sciences
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Description Logics are knowledge representation formalisms which have been used in a wide range of application domains. Owing to their appealing expressiveness, we consider in this paper extensions of the well-known concept language ALC allowing for number restrictions on complex role expressions. These have been first introduced by Baader and Sattler as ALCN(M) languages, with the adoption of role constructors M ⊆ {o,-, ⊔,⊓}. In particular, as far as languages equipped with role composition are concerned, they showed in 1999 that, although ALCN(o) is decidable, the addition of other operators may easily lead to undecidability: in fact, ALCN(o,⊓) and ALCN(o,-,⊔) were proved undecidable. In this work, we further investigate the computational properties of the ALCN family, aiming at narrowing the decidability gap left open by Baader and Sattler's results. In particular, we will show that ALCN(o) extended with inverse roles both in number and in value restrictions becomes undecidable, whereas it can be safely extended with qualified number restrictions without losing decidability of reasoning.