The Description Logic EL is used to formulate several large biomedical ontologies. Fuzzy extensions of EL can express the vagueness inherent in many biomedical concepts. We study the reasoning problem of deciding positive subsumption in fuzzy EL with semantics based on general t-norms. We show that the complexity of this problem depends on the specific t-norm chosen. More precisely, if the t-norm has zero divisors, then the problem is co-NP-hard; otherwise, it can be decided in polynomial time. We also show that the best subsumption degree cannot be computed in polynomial time if the t-norm contains the Łukasiewicz t-norm.

We study probabilistic variants of the description logic EL. For the case where probabilities apply only to concepts, we provide a careful analysis of the borderline between tractability and ExpTime-completeness. One outcome is that any probability value except zero and one leads to intractability in the presence of general TBoxes, while this is not the case for classical TBoxes. For the case where probabilities can also be applied to roles, we show PSpace-completeness. This result is (positively) surprising as the best previously known upper bound was 2-ExpTime and there were reasons to believe in completeness for this class.