Ordinal Conditional Functions for Nearly Counterfactual Revision

TL;DR

This paper introduces a novel belief revision framework using Ordinal Conditional Functions with infinite values to handle nearly counterfactual scenarios, enabling more nuanced updates of beliefs when certain antecedents are almost certainly false.

Contribution

It proposes a new model of belief revision that incorporates infinite-valued ordinal functions to better represent and update beliefs in nearly counterfactual situations.

Findings

Model captures intuition that some antecedents cannot be validated

Uses simple arithmetical operations for belief change

Framework allows finite belief improvement in complex scenarios

Abstract

We are interested in belief revision involving conditional statements where the antecedent is almost certainly false. To represent such problems, we use Ordinal Conditional Functions that may take infinite values. We model belief change in this context through simple arithmetical operations that allow us to capture the intuition that certain antecedents can not be validated by any number of observations. We frame our approach as a form of finite belief improvement, and we propose a model of conditional belief revision in which only the "right" hypothetical levels of implausibility are revised.