  This paper revisits the multi-agent epistemic logic presented in [10], where
agents and sets of agents are replaced by abstract, intensional "names". We
make three contributions. First, we study its model theory, providing adequate
notions of bisimulation and frame morphisms, and use them to study the logic's
expressive power and definability. Second, we show that the logic has a natural
neighborhood semantics, which in turn allows to show that the axiomatization in
[10] does not rely on possibly controversial introspective properties of
knowledge. Finally, we extend the logic with common and distributed knowledge
operators, and provide a sound and complete axiomatization for each of these
extensions. These results together put the original epistemic logic with names
in a more modern context and opens the door for a logical analysis of epistemic
phenomena where group membership is uncertain or variable.
