Parallel Belief Contraction via Order Aggregation

2025-01-23

AI Summary

This paper investigates iterative belief contraction under *synchronous batch deletion* of multiple information items, overcoming limitations of conventional parallel contraction models that assume single-step operations and weak rationality constraints. Methodologically, it introduces the first general framework enabling the migration of *strong rationality meta-conditions*—including systematicity, consistency, and minimal change—to parallel, multi-step settings. It extends serial iterative belief change to the parallel setting via a novel construction based on *n-ary TeamQueue-order aggregation*, semantically modeling successive batch deletions. Integrating belief revision logic with iterative change theory, the paper formally defines and constructs a family of *iterative parallel contraction operators* satisfying strong rationality. The resulting operators precisely characterize the dynamic evolution of belief states under repeated, concurrent information removal.

Technology Category

• Knowledge Representation and Reasoning: Reasoning with Beliefs
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Multiagent Systems: Agreement, Argumentation & Negotiation

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• Belief System Dynamics
• Parallel Information Removal
• Adaptive Adjustment

Innovation

• Parallel Belief Change
• Multiple Information Removal
• Booth and Chandler's Tool