KNOWING WHETHER, KNOWING THAT, AND THE CARDINALITY OF STATE-SPACES

We introduce a new knowledge operator called ''knowing whether.'' Know ing whether an event occurred means either knowing that it occurred or knowing that it did not occur. We demonstrate the following differenc e between ''knowing whether'' and ''knowing that.'' In a multiple agen t model, a sequence of events generated by successively applying ''kno wing that'' operators, or their negations, may be contradictory. But w hen ''knowing whether'' operators are used instead, the sequence is ne ver contradictory. Using this property of the ''knowing whether'' oper ator we construct a multiple agent model with a continuum of knowledge states. This simplifies such a construction due to Aumann [1]. Journa l of Economic Literature Classification Number: D80. (C) 1996 Academic Press. inc.