E-connections of Description Logics

1 Motivation Combining description logics (DLs) with other logical formalisms, including other DLs, is an important and challenging task. Recent examples include: 1. the combination of DLs with temporal logics to form multi-dimensional temporal DLs, cf. e.g. [1, 6, 10]; 2. the fusion of multiple DLs into a single formalism that inherits decidability from its components, cf. [2]; 3. the combination of different DLs in the context of loosely federated information systems resulted in distributed description logics (DDLs), cf. [4]. A relatively new technique of combining description logics, first proposed in [9], is the formation of so-called E-connections. The general idea behind this combination method is that the interpretation domains of the connected logics are disjoint and interconnected by means of link relations. The language of the E-connection is then the union of the original languages enriched with operators capable of talking about the link relations. To illustrate this idea, let us consider the E-connection of the two description logics ALCQI and ALCIO. Assume that we have two knowledge bases: one deals with people and uses ALCQI; the other deals with countries and employs ALCIO. Note that such a scenario is quite natural: it may be the case that the two knowledge bases have been developed independently and are now required to interoperate—this situation is standard for loosely