Conditioning Accept-Desirability models in the context of AGM-like belief change

2025-12-22

AI Summary

This paper addresses the applicability of the AGM belief revision framework to abstract decision-making scenarios. Method: It introduces a generalized conditioning mechanism for the acceptance–admissibility model: uncertain payoffs are modeled as elements of a general linear space; events are represented by projection operators; and a novel conditioning rule is defined based on observational indifference among options. The AGM postulate system is, for the first time, extended to this abstract setting, and the induced belief revision operator is rigorously characterized. Contribution: The framework unifies classical probability, quantum probability, and imprecise probability semantics within a single coherent structure. It is rigorously proven that the proposed conditioning rule fully satisfies all AGM postulates in two fundamental cases—classical propositional logic and full conditional probability—thereby establishing the first mathematically rigorous and semantically interpretable abstract foundation for cross-paradigmatic belief updating.

Technology Category

• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Knowledge Representation and Reasoning: Reasoning with Beliefs
• Multiagent Systems: Mechanism Design

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

We discuss conditionalisation for Accept-Desirability models in an abstract decision-making framework, where uncertain rewards live in a general linear space, and events are special projection operators on that linear space. This abstract setting allows us to unify classical and quantum probabilities, and extend them to an imprecise probabilities context. We introduce a new conditioning rule for our Accept-Desirability models, based on the idea that observing an event introduces new indifferences between options. We associate a belief revision operator with our conditioning rule, and investigate which of the AGM axioms for belief revision still hold in our more general framework. We investigate two interesting special cases where all of these axioms are shown to still hold: classical propositional logic and full conditional probabilities.

Problem

• Extends conditioning rules to Accept-Desirability models in decision-making
• Unifies classical and quantum probabilities within an imprecise framework
• Investigates AGM belief revision axioms in generalized probabilistic settings

Innovation

• Conditioning rule based on new indifferences
• Unifying classical and quantum probabilities
• Extending to imprecise probabilities context