Belief Revision in a Probabilistic Setting

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.