Adding Threshold Concepts to the Description Logic $\mathcal{EL}$

Abstract

We introduce an extension of the lightweight Description Logic $\mathcal{EL}$ 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 $\mathcal{EL}$ concepts to construct a specific graded membership function deg, and investigate the complexity of reasoning in the Description Logic $\tau\mathcal{EL}$deg, which extends $\mathcal{EL}$ by threshold concepts defined using deg. We also compare the instance problem for threshold concepts of the form C _> t in $\tau\mathcal{EL}$deg with the relaxed instance queries of Ecke et al.