Approximate Deduction in Single Evidential Bodies

TL;DR

This paper explores methods for approximate deduction within the Dempster-Shafer evidence calculus and interval probability theory, focusing on integrating conditional and unconditioned knowledge efficiently.

Contribution

It introduces formulas for combining conditional and unconditioned probability estimates under different interpretations, notably a belief-oriented approach that simplifies computation.

Findings

Developed formulas for evidence integration under various interpretations.

Proposed a belief-oriented method incorporating modus ponens and tollens.

Achieved direct elementary mass distribution outputs without iterative approximation.

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.