This paper presents a non-numeric approach to uncertain reasoning by extending the incidence calculus. In parallel to the well known fuzzy, belief/plausibility, probability, and necessity/possibility measures, the corresponding classes of non-numeric functions are examined. A method of constructing non-numeric functions is discussed using the notion of compatibility relations. Non-numeric functions are used to interpret uncertain reasoning by providing possible-worlds semantics for both qualitative and quantitative methods.INDEX TERMS: Belief/plausibility, fuzzy measure, incidence calculus, interval structure, necessity/possibility, probability, non-numeric functions, rough sets, uncertain reasoning.

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