  Probability measures by themselves, are known to be inappropriate for
modeling the dynamics of plain belief and their excessively strong
measurability constraints make them unsuitable for some representational tasks,
e.g. in the context of firstorder knowledge. In this paper, we are therefore
going to look for possible alternatives and extensions. We begin by delimiting
the general area of interest, proposing a minimal list of assumptions to be
satisfied by any reasonable quasi-probabilistic valuation concept. Within this
framework, we investigate two particularly interesting kinds of quasi-measures
which are not or much less affected by the traditional problems. * Ranking
measures, which generalize Spohn-type and possibility measures. * Cumulative
measures, which combine the probabilistic and the ranking philosophy, allowing
thereby a fine-grained account of static and dynamic belief.
