First Order Common Knowledge Logics

In this paper we investigate rst order common knowledge logics; i.e., modal epistemic logics based on rst order logic with common knowledge operators. It is shown that even rather weak fragments of rst order common knowledge logics are not recursively axiomatizable. This applies, for example, to fragments which allow to reason about names only; that is to say, fragments the rst order part of which is based on constant symbols and the equality symbols only. Then formal properties of \quantifying into" epistemic contexts are investigated. The results are illustrated by means of epistemic representations of Nash Equilibria for nite games with mixed strategies.