A SOUND INTERPRETATION OF MINIMALITY PROPERTIES OF COMMON BELIEF IN MINIMAL SEMANTICS

A soundness proof for an axiomatization of common belief in minimal ne ighbourhood semantics is provided, thereby leaving aside all assumptio ns of monotonicity in agents' reasoning. 'Minimality' properties of co mmon belief are thus emphasized, in contrast to the more usual 'fixed point' properties. The proof relies on the existence of transfinite fi xed points of sequences of neighbourhood systems even when they are no t closed under supersets. Obvious shortcoming of the note is the lack of a completeness proof.