This paper presents a non-numeric approach to uncertain reasoning by e
xtending 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 met
hod of constructing non-numeric functions is discussed using the notio
n of compatibility relations. Non-numeric functions are used to interp
ret uncertain reasoning by providing possible-worlds semantics for bot
h qualitative and quantitative methods.