Coherence of Dempster's conditioning rule in discrete possibilistic Markovmodels

We consider discrete possibilistic systems for which the available informat ion is given by one-step transition possibilities and initial possibilities . These systems can be represented, or modelled, by a collection of variabl es satisfying a possibilistic counterpart of the Markov condition. This mea ns that, given the values assumed by a selection of variables, the possibil ity that a subsequent variable assumes some value only depends on the value taken by the most recent variable of the selection. The one-step transitio n possibilities are recovered by computing the conditional possibility of a ny two consecutive variables. Under the behavioural interpretation as margi nal betting rates against events these 'conditional' possibilities and the initial possibilities should satisfy the rationality criteria of 'avoiding sure loss' and 'coherence'. We show that this is indeed the case when the c onditional possibilities are defined using Dempster's conditioning rule.