Adding threshold concepts to the description logic εL

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 individual 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 Description Logic τεL(deg), which extends εL by threshold concepts defined using deg. We also compare the instance problem for threshold concepts of the form C>t in TεL(deg) with the relaxed instance queries of Ecke et al.