A study of associative evidential reasoning

Associative evidential reasoning is the mechanism of combining evidence and evaluating hypotheses, which is the core of many computational systems. It is shown that under the generalized symmetry condition, that is, f(a,b)=neg (f(neg(a), neg(b))), where f is the combination operator satisfying common requirements like associativity and monotonicity, and neg maps positive elements to negative ones and vice versa, f is uniquely determined by a one-place mapping from the positive region to the set of positive reals. Furthermore, such combination formulas cannot be made robust, and quantizing the region will cause the loss of associativity or other inconsistencies. The implications on evidential reasoning system are: there exists often only one kind of formula for combining evidence; the quest for robust combination is often infeasible; and the attempt of converting numerical degrees of belief to linguistic quantifiers and vice versa is destined to be fruitless