PSpace Reasoning for DLs with Qualifying Number Restrictions

The description logic ALCQI extends the 'standard' description logic ALC by qualifying number restrictions and converse roles. We show that conept satisfiability for this DL is still decidable in polynomial space. The presented algorithm combines techniques from [Tob99a] to deal with qualifying number restrictions and from [HST99] to deal with converse roles. Additionally, we extend the result to ALCQIR, which extends ALCQI by role intersections. This solves an open problem from [DLNN97]. The result for ALCQI has already been presented in the seperate technical report [Tob99b]. In this report we use the same techniques to obtain the stronger result for ALCQIR.