``Knowing Whether,'' ``Knowing That,'' and The Cardinality of State Spaces

We introduce a new knowledge operator called ``knowing whether.'' Knowing whether an event occurred means either knowing that it occurred or knowing that it did not occur. We demonstrate the following difference between ``knowing whether'' and ``knowing that.'' In a multiple agent model, a sequence of events generated by successively applying ``knowing that'' operators, or their negations, may be contradictory. But when ``knowing whether'' operators are used instead, the sequence is never contradictory. Using this property of the ``knowing whether'' operator we construct a multiple agent model with a continuum of knowledge states. This simplifies such a construction due to Aumann [1]. Journal of Economic Literature Classification Number: D80. 1996 Academic Press, Inc.