Approximate Deduction in Single Evidential Bodies

Abstract: 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.