1. which roles may be used inside certain concept constructors, 2. which roles may be used inside certain role constructors, 3. the combination of role constructors, and
4. the role constructors that may be used inside certain concept constructors.

As an example for the first case, consider the fragment of ALC Q R+ in which transitive roles may be used in existential and universal restrictions, but not in number restrictions (see, e.g., Horrocks et al., 2000.

As the result of taking the fusion of two DLs, we will obtain DLs whose set of roles NR
is partitioned. For example, the fusion of ALC Q with ALC- 1 yields a fragment of ALC Q- 1 where N R is partitioned in two sets, say N R , and N R ,. In this fragment, the inverse role constructor and roles from NR, may not be used within qualified number restrictions, while roles from NR, may not be used inside the inverse role constructor. 2 Thus, this DL is an example for the first, the second, and the fourth case.

Now consider the DL ALCF introduced above, which does not only extend ALC f with feature (dis)agreement as a concept constructor, but also provides the role composition constructor. However, the role chains built using composition have to be comprised exclusively of features and non-functional roles may not appear inside feature (dis)agreement. Hence, ALCF is also an example for the first, second, and fourth case.

As an example for the third case, the fragment of ALC r , n in which role conjunction may not be used inside the role complement constructor is considered by Lutz and Sattler
(2000).

For these restricted DLs, we do not introduce an explicit naming scheme. Note that, in this paper, we do not deal with DLs in which the combinability of concept constructors with each other is restricted since these DLs would not fit into the framework of abstract description systems introduced in the next section. An example of such a DL would be one with atomic negation of concepts, i.e., where negation may only be applied to concept names (e.g., the DL AL discussed by Donini et al., 1997).

## 3. Abstract Description Systems

In order to define the fusion of DLs and prove general results for fusions of DLs, one needs a formal definition of what are "description logics". Since there exists a wide variety of DLs with very different characteristics, we introduce a very general formalization, which should cover all of the DLs considered in the literature, but also includes logics that would usually not be subsumed under the name DL.

## 3.1 Syntax And Semantics

The syntax of an abstract description system is given by its abstract description language, which determines a set of terms, term assertions, and object assertions. In this setting, concept descriptions are represented by terms that are built using the abstract description 2. This will become clearer once we have given a formal definition of the fusion.