Elena Vlasenko will present Farsiniamarj and Haarslev's Practical Reasoning with Qualified Number Restrictions: A Hybrid Abox Calculus for the Description Logic SHQ (http://users.encs.concordia.ca/~haarslev/publications/AICom2010.pdf).
A lot of the terminology here is specific to Description Logics, and I found this paper, A Description Logic Primer (http://arxiv.org/pdf/1201.4089.pdf), to be useful in getting a handle on what was actually happening in the featured paper. Also, as the paper is rather long, one might consider skipping to section 5 after reading the introduction on one's first pass through it.
Elena indicates that she has used this paper heavily in her own work, so I will leave it to her presentation to explain and justify it.
This should be of particular interest to those with an interest in the semantic web, logic and automated reasoning, or applications of integer linear programming.