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.