MPI-I-95-2-005

An extension of the concept description language ${\cal alc\}$ used in {\sc kl-one}-like terminological reasoning is presented. The extension includes multi--modal operators that can either stand for the usual role quantifications or for modalities such as belief, time etc. The modal operators can be used at all levels of the concept terms, and they can be used to modify both concepts and roles. This is an instance of a new kind of combination of modal logics where the modal operators of one logic may operate directly on the operators of the other logic. Different versions of this logic are investigated and various results about decidability and undecidability are presented. The main problem, however, decidability of the basic version of the logic, remains open.

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Forthcoming in the {\em Journal of Applied Non-Classical Logics}