  Results on approximate deduction in the context of the calculus of evidence
of Dempster-Shafer and the theory of interval probabilities are reported.
Approximate conditional knowledge about the truth of conditional propositions
was assumed available and expressed as sets of possible values (actually
numeric intervals) of conditional probabilities. Under different
interpretations of this conditional knowledge, several formulas were produced
to integrate unconditioned estimates (assumed given as sets of possible values
of unconditioned probabilities) with conditional estimates. These formulas are
discussed together with the computational characteristics of the methods
derived from them. Of particular importance is one such evidence integration
formulation, produced under a belief oriented interpretation, which
incorporates both modus ponens and modus tollens inferential mechanisms, allows
integration of conditioned and unconditioned knowledge without resorting to
iterative or sequential approximations, and produces elementary mass
distributions as outputs using similar distributions as inputs.
