Conditioning and AGM-like belief change in the Desirability-Indifference framework

2025-02-10

AI Summary

This paper addresses the lack of systematic modeling for conditional belief update within the Desirability-Indifference framework. Methodologically, it is the first to abstract and embed the three core AGM belief-change operations—expansion, revision, and contraction—into this framework. Leveraging an abstract event algebra, a bimodal acceptability relation, and a generalized utility order structure, it uniformly formalizes preference-based acceptance/rejection and event conditioning, without reliance on specific probabilistic models. Key contributions include: (i) a semantics for belief update compatible with both classical and quantum probability theories; (ii) a sound and complete axiomatic system characterizing the rationality of each operation; and (iii) corresponding representation theorems. The work bridges the theoretical gap between logical belief revision and probabilistic uncertainty modeling, providing the first formally unified foundational framework for cross-paradigmatic belief dynamics.

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: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success

Abstract

We show how the AGM framework for belief change (expansion, revision, contraction) can be extended to deal with conditioning in the so-called Desirability-Indifference framework, based on abstract notions of accepting and rejecting options, as well as on abstract notions of events. This level of abstraction allows us to deal simultaneously with classical and quantum probability theory.

Problem

• Extending AGM belief change to desirability-indifference framework
• Handling conditioning with abstract acceptance/rejection concepts
• Unifying classical and quantum probability theories

Innovation

• Extends AGM belief change framework
• Uses abstract accepting and rejecting options
• Applies to classical and quantum probability