A logic to reason about likelihood
Artificial Intelligence
Some algebraic and geometric computations in PSPACE
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
An analysis of first-order logics of probability
Artificial Intelligence
Reasoning about knowledge and probability
Journal of the ACM (JACM)
Fuzzy logic of Lukasiewicz logic: a clarification
Fuzzy Sets and Systems
Complexity of Terminological Reasoning Revisited
LPAR '99 Proceedings of the 6th International Conference on Logic Programming and Automated Reasoning
Modal probability, belief, and actions
Fundamenta Informaticae
Complexity of fuzzy probability logics II
Fuzzy Sets and Systems
Expressive probabilistic description logics
Artificial Intelligence
Top-k Retrieval in Description Logic Programs Under Vagueness for the Semantic Web
SUM '07 Proceedings of the 1st international conference on Scalable Uncertainty Management
Managing uncertainty and vagueness in description logics for the Semantic Web
Web Semantics: Science, Services and Agents on the World Wide Web
FOSSACS '09 Proceedings of the 12th International Conference on Foundations of Software Science and Computational Structures: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009
On Improving the Scalability of Checking Satisfiability in Probabilistic Description Logics
SUM '09 Proceedings of the 3rd International Conference on Scalable Uncertainty Management
Finite Satisfiability in Infinite-Valued Łukasiewicz Logic
SUM '09 Proceedings of the 3rd International Conference on Scalable Uncertainty Management
Reasoning within fuzzy description logics
Journal of Artificial Intelligence Research
Reasoning with very expressive fuzzy description logics
Journal of Artificial Intelligence Research
Making fuzzy description logic more general
Fuzzy Sets and Systems
Reasoning with the finitely many-valued Łukasiewicz fuzzy Description Logic SROIQ
Information Sciences: an International Journal
Syntactic labelled tableaux for Łukasiewicz fuzzy ALC
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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Uncertainty and vagueness are pervasive phenomena in real-life knowledge. They are supported in extended description logics that adapt classical description logics to deal with numerical probabilities or fuzzy truth degrees. While the two concepts are distinguished for good reasons, they combine in the notion of probably, which is ultimately a fuzzy qualification of probabilities. Here, we develop existing propositional logics of fuzzy probability into a full-blown description logic, and we show decidability of several variants of this logic under Łukasiewicz semantics. We obtain these results in a novel generic framework of fuzzy coalgebraic logic; this enables us to extend our results to logics that combine crisp ingredients including standard crisp roles and crisp numerical probabilities with fuzzy roles and fuzzy probabilities.