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Results on approximate deduction in the context of the calculus of evidenceof Dempster-Shafer and the theory of interval probabilities are reported.Approximate conditional knowledge about the truth of conditional propositionswas assumed available and expressed as sets of possible values (actuallynumeric intervals) of conditional probabilities. Under differentinterpretations of this conditional knowledge, several formulas were producedto integrate unconditioned estimates (assumed given as sets of possible valuesof unconditioned probabilities) with conditional estimates. These formulas arediscussed together with the computational characteristics of the methodsderived from them. Of particular importance is one such evidence integrationformulation, produced under a belief oriented interpretation, whichincorporates both modus ponens and modus tollens inferential mechanisms, allowsintegration of conditioned and unconditioned knowledge without resorting toiterative or sequential approximations, and produces elementary massdistributions as outputs using similar distributions as inputs.

Approximate Deduction in Single Evidential Bodies