Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Parallel Belief Contraction via Order Aggregation

Jake Chandler, Richard Booth

TL;DR

The paper addresses extending AGM-style belief contraction to parallel and iterated parallel change. It introduces an n-ary TeamQueue aggregation framework to lift serial contraction operators into the parallel domain. Key results include an axiomatic characterization of n-ary TeamQueue aggregators, the connection between the STQ variant and rational closure, and a concrete formulation of iterated parallel contraction. The approach offers a principled, scalable method for parallel belief change with potential applications beyond belief revision, including judgment and preference aggregation.

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.

Parallel Belief Contraction via Order Aggregation

TL;DR

The paper addresses extending AGM-style belief contraction to parallel and iterated parallel change. It introduces an n-ary TeamQueue aggregation framework to lift serial contraction operators into the parallel domain. Key results include an axiomatic characterization of n-ary TeamQueue aggregators, the connection between the STQ variant and rational closure, and a concrete formulation of iterated parallel contraction. The approach offers a principled, scalable method for parallel belief change with potential applications beyond belief revision, including judgment and preference aggregation.

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.
Paper Structure (12 sections, 27 theorems, 1 equation, 1 figure)

This paper contains 12 sections, 27 theorems, 1 equation, 1 figure.

Table of Contents

  1. Introduction
  2. Serial belief contraction
  3. Single-step serial change
  4. Iterated serial contraction
  5. Background on parallel belief contraction
  6. TeamQueue aggregation
  7. Construction
  8. Characterisation
  9. Further properties
  10. The connection to rational closure
  11. Parallel contraction via TeamQueue aggregation
  12. Concluding comments

Key Result

Theorem 1

Let $\odiv$ be a parallel contraction operator such that, for some serial contraction operator $\div$ that satisfies $(\mathrm{K}{1}^{ \div})$-$(\mathrm{K}{6}^{ \div})$, $\odiv$ and $\div$ jointly satisfy $(\mathrm{Int}_{\mathrm{b}}^{\odiv})$. Then $\odiv$ satisfies:

Figures (1)

  • Figure 1: Illustration of the $\oplus_{\mathrm{STQ}}$ and $\oplus_{\min}$ aggregations in Example \ref{['eg:STQvsMinRank']}. Boxes represent TPOs, with lower case letters arranged such that a lower letter corresponds to a lower world in the relevant ordering.

Theorems & Definitions (37)

  • Theorem 1
  • Proposition 1
  • Example 1
  • Theorem 2
  • Example 2
  • Definition 1
  • Definition 2
  • Definition 3
  • Example 3
  • Theorem 3
  • ...and 27 more