POSSIBILITY THEORY .2. CONDITIONAL POSSIBILITY

It is shown that the notion of conditional possibility can be consiste ntly introduced in possibility theory, in very much the same way as co nditional expectations and probabilities are defined in the measure- a nd integral-theoretic treatment of probability theory. I write down po ssibilistic integral equations which are formal counterparts of the in tegral equations used to define conditional expectations and probabili ties, and use their solutions to define conditional possibilities. In all, three types of conditional possibilities, with special cases, are introduced and studied. I explain why, like conditional expectations, conditional possibilities are not uniquely defined, but can only be d etermined up to almost everywhere equality, and I assess the consequen ces of this nondeterminacy. I also show that this approach solves a nu mber of consistency problems, extant in the literature.