Approximate reasoning maps predicates (or, equivalently, sets) to “quantitative” capacities, that is, numerical values that can be interpreted as probabilities, degrees of belief, or similar. This interpretation crucially depends on the fact that the capacity range provides certain numerical capabilities on which a number of notions are based that are only meaningful in a numerical setting.

This paper generalizes the concept to “qualitative” capacities, elements of a finite totally ordered set that only provides a minimum and a maximum. Nevertheless, qualitative counterparts of many quantitative notions can be defined by describing some qualitative capacities as possibility measures (for example, the degree of plausibility of some information) and necessity measures (for example, the degree of implausibility of some information). Since the measures are discrete, however, only relative ordering, not numerical comparison, is possible; qualitative capacities thus crucially differ from numerical belief functions.

The core contribution of the paper is the formal elaboration of the analogy between qualitative capacities and imprecise possibilities, proving that any capacity is either a lower possibility or an upper necessity measure. Furthermore, the authors present an algorithm to compute from a qualitative capacity of the first kind a representation by possibility distributions; they provide an axiomatic characterization of the theory of qualitative capacities; and they finally give a sound and complete modal logic. While being very technical, the paper elaborates its theory in a comprehensive manner and relates it to classical work; future interesting research directions include the evaluation of the quantity of information contained in a qualitative capacity.