Semantics for multi-agent only knowing: extended abstract

The paper presents a Kripke semantics for a multi-agent generalization of Levesque’s logic of “only knowing”. We prove soundness and completeness and show that the logic has the Finite model property. The logic satisfies a Modal reduction theorem to the effect that any complex syntactical representation can be syntactically reduced to a provably equivalent form which directly reflects all the models of the representation. The model theory is illustrated by means of an example of supernormal defaults in a multi-agent language.