Extending Description Logics with Generic Concepts – the Tale of Two Semantics

Description Logic (DL) ontologies often need to model similar properties for different concepts. Taking inspiration from generic classes in object-oriented programming, we introduce concept parameters to describe related concepts. For example, LocalAnesthesia[Eye] and LocalAnesthesia[Knee] can be used to describe the anesthesia of an eye or a knee, respectively. The main benefit of generic concepts is to be able to describe general properties, for example, that every local anesthesia is done by applying an anesthetic drug. We propose to use generic concepts, such as LocalAnesthesia[X] to define such properties, where a concept variable X can be replaced with suitable concepts. To capture the intended meaning of generic concepts, we define two semantics for this extension: the schema semantics, in which concept variables represent arbitrary concepts from a specific language, and the second-order semantics, in which variables represent arbitrary subsets of the domain. Generally, the second-order semantics gives more logical consequences, but the schema semantics allows a reduction to the classical DL reasoning. To combine the benefits of both semantics, we define a useful extension of the DL EL, for which both semantics coincide, and a further restriction in which the entailment problem is decidable.