Quantitative Methods for Similarity in Description Logics

Description logics (DLs) are a family of logic-based knowledge representation languages used to describe the knowledge of an application domain and reason about it in a formally well-defined way. However, all classical DLs have in common that they can only express exact knowledge, and correspondingly only allow exact inferences. In practice though, knowledge is rarely exact. Many definitions have exceptions or are vaguely formulated in the first place, and people might not only be interested in exact answers, but also in alternatives that are “close enough”. We are interested in tackling how to express that something is “close enough”, and how to integrate this notion into the formalism of DLs. To this end we employ the notion of similarity and dissimilarity measures, we will look at how useful measures can be defined in the context of DLs and two particular applications: Relaxed instance queries will use a similarity measure in order to not just give the exact answer to some query, but all answers that are reasonably similar. Prototypical definitions on the other hand use a measure of dissimilarity or distance between concepts in order to allow the definitions of and reasoning with concepts that capture not just those individuals that satisfy exactly the stated properties, but also those that are “close enough”.