The description logic handbook: theory, implementation, and applications
The description logic handbook: theory, implementation, and applications
Managing uncertainty and vagueness in description logics for the Semantic Web
Web Semantics: Science, Services and Agents on the World Wide Web
Fuzzy description logics under Gödel semantics
International Journal of Approximate Reasoning
Reasoning within fuzzy description logics
Journal of Artificial Intelligence Research
Fuzzy description logics with general t-norms and datatypes
Fuzzy Sets and Systems
Making fuzzy description logic more general
Fuzzy Sets and Systems
Fuzzy Description Logics and t-norm based fuzzy logics
International Journal of Approximate Reasoning
Reasoning with the finitely many-valued Łukasiewicz fuzzy Description Logic SROIQ
Information Sciences: an International Journal
On the failure of the finite model property in some Fuzzy Description Logics
Fuzzy Sets and Systems
Description logics over lattices with multi-valued ontologies
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
How fuzzy is my fuzzy description logic?
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
A tableau algorithm for fuzzy description logics over residuated de morgan lattices
RR'12 Proceedings of the 6th international conference on Web Reasoning and Rule Systems
On the (un)decidability of fuzzy description logics under Łukasiewicz t-norm
Information Sciences: an International Journal
Aggregation operators for fuzzy ontologies
Applied Soft Computing
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The combination of Fuzzy Logics and Description Logics (DLs) has been investigated for at least two decades because such fuzzy DLs can be used to formalize imprecise concepts. In particular, tableau algorithms for crisp Description Logics have been extended to reason also with their fuzzy counterparts. Recently, it has been shown that, in the presence of general concept inclusion axioms (GCIs), some of these fuzzy DLs actually do not have the finite model property, thus throwing doubt on the correctness of tableau algorithm for which it was claimed that they can handle fuzzy DLs with GCIs. In a previous paper, we have shown that these doubts are indeed justified, by proving that a certain fuzzy DL with product t-norm and involutive negation is undecidable. In the present paper, we show that undecidability also holds if we consider a t-norm-based fuzzy DL where disjunction and involutive negation are replaced by the constructor implication, which is interpreted as the residuum. The only condition on the t-norm is that it is a continuous t-norm "starting" with the product t-norm, which covers an uncountable family of t-norms.