Parallel Belief Contraction via Order Aggregation

TL;DR

This paper introduces a novel method for extending serial belief contraction operators to handle parallel belief change, using an n-ary generalization of order aggregation, and explores their behavior over sequences of such contractions.

Contribution

It proposes a new approach to extend serial belief contraction operators to parallel cases using order aggregation, and analyzes their iterative behavior.

Findings

Develops a general method for parallel belief contraction extension.

Utilizes n-ary generalization of TeamQueue order aggregators.

Analyzes behavior of beliefs after sequences of parallel contractions.

Abstract

The standard ``serial'' (aka ``singleton'') model of belief contraction models the manner in which an agent's corpus of beliefs responds to the removal of a single item of information. One salient extension of this model introduces the idea of ``parallel'' (aka ``package'' or ``multiple'') change, in which an entire set of items of information are simultaneously removed. Existing research on the latter has largely focussed on single-step parallel contraction: understanding the behaviour of beliefs after a single parallel contraction. It has also focussed on generalisations to the parallel case of serial contraction operations whose characteristic properties are extremely weak. Here we consider how to extend serial contraction operations that obey stronger properties. Potentially more importantly, we also consider the iterated case: the behaviour of beliefs after a sequence of parallel contractions. We propose a general method for extending serial iterated belief change operators to handle parallel change based on an n-ary generalisation of Booth & Chandler's TeamQueue binary order aggregators.