Multi-Agent Only-Knowing Revisited
  Levesque introduced the notion of only-knowing to precisely capture the
beliefs of a knowledge base. He also showed how only-knowing can be used to
formalize non-monotonic behavior within a monotonic logic. Despite its appeal,
all attempts to extend only-knowing to the many agent case have undesirable
properties. A belief model by Halpern and Lakemeyer, for instance, appeals to
proof-theoretic constructs in the semantics and needs to axiomatize validity as
part of the logic. It is also not clear how to generalize their ideas to a
first-order case. In this paper, we propose a new account of multi-agent
only-knowing which, for the first time, has a natural possible-world semantics
for a quantified language with equality. We then provide, for the propositional
fragment, a sound and complete axiomatization that faithfully lifts Levesque's
proof theory to the many agent case. We also discuss comparisons to the earlier
approach by Halpern and Lakemeyer.
