A Parametric Approach to Deductive Databases with Uncertainty
IEEE Transactions on Knowledge and Data Engineering
P-SHOQ(D): A Probabilistic Extension of SHOQ(D) for Probabilistic Ontologies in the Semantic Web
JELIA '02 Proceedings of the European Conference on Logics in Artificial Intelligence
The description logic handbook: theory, implementation, and applications
The description logic handbook: theory, implementation, and applications
Uncertainty management for description logic-based ontologies
Uncertainty management for description logic-based ontologies
General Concept Inclusions in Fuzzy Description Logics
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
Reasoning within fuzzy description logics
Journal of Artificial Intelligence Research
Reasoning with very expressive fuzzy description logics
Journal of Artificial Intelligence Research
A correspondence theory for terminological logics: preliminary report
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
P-CLASSIC: a tractable probablistic description logic
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Fuzzy Description Logic Reasoning Using a Fixpoint Algorithm
LFCS '09 Proceedings of the 2009 International Symposium on Logical Foundations of Computer Science
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We present a reasoning procedure for ontologies with uncertainty described in Description Logic (DL) which include General TBoxes, i.e., include cycles and General Concept Inclusions (GCIs). For this, we consider the description language ${{\cal{ALC}}_U}$, in which uncertainty parameters are associated with ABoxes and TBoxes, and which allows General TBoxes. Using this language as a basis, we then present a tableau algorithm which encodes the semantics of the input knowledge base as a set of assertions and linear and/or nonlinear arithmetic constraints on certainty variables. By tuning the uncertainty parameters in the knowledge base, different notions of uncertainty can be modeled and reasoned with, within the same framework. Our reasoning procedure is deterministic, and hence avoids possible empirical intractability in standard DL with General TBoxes. We further illustrate the need for blocking when reasoning with General TBoxes in the context of ${{\cal{ALC}}_U}$.