Belief Revision in a Probabilistic Setting

Abstract

This work develops an approach to qualitative belief revision in a fully probabilistic setting. We begin with a logic where possible worlds are assigned probabilities. In this logic an agent may believe a formula is true even though the subjective probability of the formula is less than 1.0. Similarly, after revision by a formula ϕ, the agent will believe ϕ is true, even though the agent’s subjective probability of ϕ may be less than 1.0. We establish a correspondence with the hallmark AGM postulates for belief revision. Moreover, we use Jeffrey Conditionalisation to establish a link with iterated belief change. To this end, we develop an approach that satisfies appropriately modified Darwiche-Pearl postulates (with clear justification). Thus, we provide a connection between quantitative probabilistic approaches on the one hand and the qualitative formulation of belief change, on the other. This work holds potential for the development of practical belief revision systems by applying a (qualitative) approach to belief change in probabilistic, uncertain domains.

Authors 4

1. James P. Delgrande

   Simon Fraser University

   Affiliation as printed

   Simon Fraser University

2. Gerhard Lakemeyer Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University

3. Maurice Pagnucco

   UNSW Sydney

   Affiliation as printed

   The University of New South Wales

4. Joshua Sack

   California State University, Long Beach

   Affiliation as printed

   California State University Long Beach