General Belief Measures

Probability measures by themselves are known to be inappropriate for modeling the dynamics of plain belief and their excessively s�ong measura­ bility constraints make them unsmtable for some representational tasks, e.g. in the context of frrst­ order knowledge. In this paper, we are therefore going to look for possible alternatives and ex­ tensions. We begin by delimiting the general area of interest, proposing a minimal list of as�ump­ tions to be satisfied by any reasonable quasi-pro­ babilistic valuation concept. Within this frame­ work, we investigate two particularly interesting kinds of quasi-measures which are not or much less affected by the traditional problems. • Ranking measures, which generalize Spohntype and possibility measure�. . • Cumulative measures, wh1ch combme the pro­ babilistic and the ranking philosophy, allowing thereby a fine-grained account of static and dy­