On perfect introspection with Quantifying-in

1 I n t r o d u c t i o n In areas such as artificial intelligence or distributed systems, there has been considerable interest in agents with perfect introspection, that is, agents, who know everything they know and if they don't know something, then they know that they don't know it. For example, the so-called autoepistemic logics developed in artificial intelligence use introspection to model certain forms of nonmonotonic reasoning(e.g. [Moo85, Kon88, MT89]). In distributed systems, perfect introspection has been found useful in modeling the knowledge ascribed to the various components of a system (e.g. [HM90]). The most widely used formalism to model the beliefs of introspective agents is possibleworld semantics [Kri63], whose application to knowledge and belief 1 goes back to Hin1In this paper, the distinction between knowledge and belief is not important. Hence we will use the two terms interchangeably.