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 Lukasiewicz t-norm.
Borgwardt, S., PENALOZA NYSSEN, R. (2013). Positive Subsumption in Fuzzy EL with General t-norms. In Proceedings of the 23rd International Joint Conference on Artificial Intelligence (IJCAI'13) (pp.789-795). AAAI Press.
Positive Subsumption in Fuzzy EL with General t-norms
PENALOZA NYSSEN, RAFAEL
2013
Abstract
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 Lukasiewicz t-norm.
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