Abstract

Abstract. We introduce an extension of the lightweight Description Logic EL that allows us to define concepts in an approximate way. For this purpose, we use a graded membership function, which for each in-dividual and concept yields a number in the interval [0, 1] expressing the degree to which the individual belongs to the concept. Threshold concepts C∼t for ∼ ∈ {<,≤,>,≥} then collect all the individuals that belong to C with degree ∼ t. We generalize a well-known characterization of membership in EL concepts to construct a specific graded membership function deg, and investigate the complexity of reasoning in the Descrip-tion Logic τEL(deg), which extends EL by threshold concepts defined using deg. We also compare the instance problem for threshold concepts of the form C>t in τEL(deg) with the relaxed instance queries of Ecke et al. 1