Rules, Belief Functions and Default Logic

TL;DR

This paper introduces a belief function framework for rules, integrating default logic and Dempster-Shafer theory, and demonstrates its generalization and connection to Reiter's Default Logic.

Contribution

It presents a unified belief function approach to rules, including default and non-monotonic rules, and links it to existing logical formalisms like Reiter's Default Logic.

Findings

Belief functions can represent various rule types including default and non-monotonic rules.

Dempster-Shafer theory is justified for certain rule representations under independence assumptions.

Default logic emerges as a special case within the belief function framework.

Abstract

This paper describes a natural framework for rules, based on belief functions, which includes a repre- sentation of numerical rules, default rules and rules allowing and rules not allowing contraposition. In particular it justifies the use of the Dempster-Shafer Theory for representing a particular class of rules, Belief calculated being a lower probability given certain independence assumptions on an underlying space. It shows how a belief function framework can be generalised to other logics, including a general Monte-Carlo algorithm for calculating belief, and how a version of Reiter's Default Logic can be seen as a limiting case of a belief function formalism.