An Interpretation of Belief Functions by means of a Probabilistic Multi-modal Logic

TL;DR

This paper explores a probabilistic interpretation of belief functions using a multi-modal logic framework, introducing an adaptive rule for conflict management and source independence based on entropy maximization.

Contribution

It presents a novel probabilistic interpretation of belief functions through a logical framework and introduces an adaptive rule for conflict handling and source independence.

Findings

Derived an adaptive conjunctive rule from logical principles

Implemented a probabilistic multi-modal logic for belief functions

Proposed a source independence concept based on entropy maximization

Abstract

While belief functions may be seen formally as a generalization of probabilistic distributions, the question of the interactions between belief functions and probability is still an issue in practice. This question is difficult, since the contexts of use of these theory are notably different and the semantics behind these theories are not exactly the same. A prominent issue is increasingly regarded by the community, that is the management of the conflicting information. Recent works have introduced new rules for handling the conflict redistribution while combining belief functions. The notion of conflict, or its cancellation by an hypothesis of open world, seems by itself to prevent a direct interpretation of belief function in a probabilistic framework. This paper addresses the question of a probabilistic interpretation of belief functions. It first introduces and implements a theoretically grounded rule, which is in essence an adaptive conjunctive rule. It is shown, how this rule is derived from a logical interpretation of the belief functions by means of a probabilistic multimodal logic; in addition, a concept of source independence is introduced, based on a principle of entropy maximization.