Eliminating concepts and roles from ontologies in expressive descriptive logics

Forgetting is an important tool for reducing ontologies by eliminating some redundant concepts and roles while
preserving sound and complete reasoning. Attempts have previously been made to address the problem of forgetting
in relatively simple description logics (DLs), such as DL-Lite and extended EL . However, the issue of forgetting
for ontologies in more expressive DLs, such as ALC and OWL DL, is largely unexplored. In particular, the problem
of characterizing and computing forgetting for such logics is still open. In this paper, we first define semantic
forgetting about concepts and roles in ALC ontologies and state several important properties of forgetting in this
setting.We then define the result of forgetting for concept descriptions in ALC, state the properties of forgetting for
concept descriptions, and present algorithms for computing the result of forgetting for concept descriptions. Unlike
the case of DL-Lite, the result of forgetting for an ALC ontology does not exist in general, even for the special case
of forgetting in TBoxes. This makes the problem of computing the result of forgetting in ALC more challenging.
We address this problem by defining a series of approximations to the result of forgetting for ALC ontologies and
studying their properties. Our algorithms for computing approximations can be directly implemented as a plug-in
of an ontology editor to enhance its ability of managing and reasoning in (large) ontologies.