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Parallel Belief Revision via Order Aggregation

Jake Chandler, Richard Booth

TL;DR

The paper tackles the gap in iterated parallel belief revision by proposing a constructive, order-aggregation-based framework using TeamQueue aggregators. It bridges serial iterated revision and parallel change, deriving plausible parallel postulates (e.g., PC3, PC4, S_b, Ind) while avoiding problematic strong principles (SC2, P_b), and shows how to extend serial revision operators via TQ to iterated parallel revision. Through STQ and related aggregation properties, it connects to rational closure and Chopra-style contraction postulates, offering a scalable method to construct iterated parallel revision operators from well-understood serial ones. The approach provides a principled, flexible foundation for future work on class characterizations, HI/LI connections, and broader constructive foundations for iterated parallel belief change.

Abstract

Despite efforts to better understand the constraints that operate on single-step parallel (aka "package", "multiple") revision, very little work has been carried out on how to extend the model to the iterated case. A recent paper by Delgrande & Jin outlines a range of relevant rationality postulates. While many of these are plausible, they lack an underlying unifying explanation. We draw on recent work on iterated parallel contraction to offer a general method for extending serial iterated belief revision operators to handle parallel change. This method, based on a family of order aggregators known as TeamQueue aggregators, provides a principled way to recover the independently plausible properties that can be found in the literature, without yielding the more dubious ones.

Parallel Belief Revision via Order Aggregation

TL;DR

The paper tackles the gap in iterated parallel belief revision by proposing a constructive, order-aggregation-based framework using TeamQueue aggregators. It bridges serial iterated revision and parallel change, deriving plausible parallel postulates (e.g., PC3, PC4, S_b, Ind) while avoiding problematic strong principles (SC2, P_b), and shows how to extend serial revision operators via TQ to iterated parallel revision. Through STQ and related aggregation properties, it connects to rational closure and Chopra-style contraction postulates, offering a scalable method to construct iterated parallel revision operators from well-understood serial ones. The approach provides a principled, flexible foundation for future work on class characterizations, HI/LI connections, and broader constructive foundations for iterated parallel belief change.

Abstract

Despite efforts to better understand the constraints that operate on single-step parallel (aka "package", "multiple") revision, very little work has been carried out on how to extend the model to the iterated case. A recent paper by Delgrande & Jin outlines a range of relevant rationality postulates. While many of these are plausible, they lack an underlying unifying explanation. We draw on recent work on iterated parallel contraction to offer a general method for extending serial iterated belief revision operators to handle parallel change. This method, based on a family of order aggregators known as TeamQueue aggregators, provides a principled way to recover the independently plausible properties that can be found in the literature, without yielding the more dubious ones.

Paper Structure

This paper contains 8 sections, 17 theorems, 1 equation, 3 figures.

Table of Contents

  1. Introduction
  2. Background on serial belief revision
  3. Background on parallel belief revision
  4. Single-step parallel revision
  5. Iterated parallel revision
  6. TeamQueue aggregation and iterated parallel contraction
  7. Parallel Revision via TeamQueue aggregation
  8. Concluding comments

Key Result

Proposition 1

Let $\circledast$ be a parallel revision operator such that, for some AGM serial revision operator $\ast$, $\circledast$ and $\ast$ jointly satisfy $(\mathrm{Conj}^{ \circledast})$. Then $(\mathrm{C}{2}^{ \circledast}_{ \preccurlyeq})$ is equivalent to:

Figures (3)

  • Figure 1: Illustration of the $\oplus_{\mathrm{STQ}}\xspace$ aggregator, using 3 inputs. Boxes represent TPOs, with lower case letters arranged such that a lower letter corresponds to a lower world in the relevant ordering.
  • Figure 2: Model of Example \ref{['ex:KPPRevise']}, using the TQ approach. The correct result is obtained here: $A, B\notin[\Psi]\xspace$ and $A\in[(\Psi\circledast \{A, B\})\circledast \{\neg B\}]\xspace$, since $\min(\preccurlyeq_{\Psi\circledast \{A, B\}}, [\![\neg B]\!]\xspace)= \{z\}\subseteq\{z, w\}=[\![A]\!]\xspace$.
  • Figure 3: Illustration of the countermodel in the proof of Proposition \ref{['prop:PFails']}.

Theorems & Definitions (25)

  • Example 1: Konieczny & Pino Pérez doi:10.1080/11663081.2000.10511003
  • Proposition 1
  • Definition 1
  • Proposition 2
  • Example 2
  • Definition 2
  • Definition 3
  • Definition 4
  • Proposition 3
  • Definition 5
  • ...and 15 more