Nonnumeric belief structures

The nonnumeric belief, a counterpart of the belief function, is defined as the lower envelope of a family of incidence mappings (i.e., the nonnumeric counterpart of probability functions). Likewise, the nonnumeric conditional belief is defined as the lower envelope of a family of conditional incidence mappings. Such definitions are consistent with the corresponding definitions for belief functions. There exists a closed-form expression for the proposed conditional nonnumeric beliefs, which is useful in qualitative, nonmonotonic reasoning, and conditional logic