The underlying idea of the equation is, if two name observations share more and closer common topics, and also these topics receive higher weights according to the current name observation set, then the two observations should be more related to each other.
the factor sim(o 1 ∩ t, o 2 ∩ t) is designed to measure the fine relatedness between o 1 and o 2 given the topic t. Sometimes, both o 1 and o 2 are mapped to t and both close to this topic, but in fact they depict different aspects of t since some of our topics are more general thus include several aspects.