The Complexity of Reasoning with Cardinality Restrictions and Nominals in Expressive Description Logics

We study the complexity of the combination of the Description Logics ALCQ and ALCQI with a terminological formalism based on cardinality restrictions on concepts. These combinations can naturally be embedded into C^2, the two variable fragment of predicate logic with counting quantifiers, which yields decidability in NExpTime. We show that this approach leads to an optimal solution for ALCQI, as ALCQI with cardinality restrictions has the same complexity as C^2 (NExpTime-complete). In contrast, we show that for ALCQ, the problem can be solved in ExpTime. This result is obtained by a reduction of reasoning with cardinality restrictions to reasoning with the (in general weaker) terminological formalism of general axioms for ALCQ extended with nominals. Using the same reduction, we show that, for the extension of ALCQI with nominals, reasoning with general axioms is a NExpTime-complete problem. Finally, we sharpen this result and show that pure concept satisfiability for ALCQI with nominals is NExpTime-complete. Without nominals, this problem is known to be PSpace-complete

Decidability of SHI with transitive closure of roles

leduc2009aInternational audienceThis paper investigates a description logic, namely SHI+, which extends SHI by adding transitive closure of roles. The resulting logic SHI+ allows transitive closure of roles to occur not only in concept inclusion axioms but also in role inclusion axioms. We show that SHI+ is decidable by devising a sound and complete algorithm for deciding satisfiability of concepts in SHI+ with respect to a set of concept and role inclusion axioms

Sharing intelligent services between homes

The user’s environment is increasingly enriched with computing devices that offer services that aid users in their daily activities. Current use of these services is either public (i.e. unrestricted), or requires explicit registration. In the first case, user control and security are sacrificed whilst in the second ease of use and flexibility is limited. In this paper, we extend the perspective of user-centric computing in offering guests a simple and transparent way to access their home services from a visited intelligent environment. We provide the users with a Personal Access Device (PAD) that facilitates creation of trust between the user’s own home and a visited intelligent environment. This enables seamless access to home services from the visited environment.Henk Eertink, Remco Poortinga, Tom Broens, Stephan Tobies, Andrew Tokmakoff, Aart van Haltere