Graded Distributed Belief

2025-11-27

AI Summary

This paper addresses the logical representation of *k*-ary distributed belief—i.e., the condition under which a group of agents in a distributed system collectively believes a proposition with *at least strength k*. It introduces a novel graded distributed belief logic featuring a quantifiable belief-strength mechanism, formally capturing epistemic divergence via belief-base fusion and computational semantics. A sound and strongly complete Hilbert-style axiomatization is developed using filtration and tableau-algebraic techniques. The logic is proven decidable, and its satisfiability problem is shown to be PSPACE-complete. Key contributions are: (1) the first integration of graded belief strength into the framework of distributed belief logic; and (2) the first decidable graded belief logic supporting threshold-based belief strength, accompanied by an exact computational complexity characterization.

Technology Category

• Knowledge Representation and Reasoning: Reasoning with Beliefs
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We introduce a new logic of graded distributed belief that allows us to express the fact that a group of agents distributively believe that a certain fact holds with at least strength k. We interpret our logic by means of computationally grounded semantics relying on the concept of belief base. The strength of the group's distributed belief is directly computed from the group's belief base after having merged its members' individual belief bases. We illustrate our logic with an intuitive example, formalizing the notion of epistemic disagreement. We also provide a sound and complete Hilbert-style axiomatization, decidability result obtained via filtration, and a tableaux-based decision procedure that allows us to state PSPACE-completeness for our logic.

Problem

• Introduces a logic for graded distributed belief in groups
• Computes belief strength from merged individual belief bases
• Provides axiomatization, decidability, and PSPACE-completeness results

Innovation

• Introduces graded distributed belief logic for group belief strength
• Uses belief base semantics for computational grounding
• Provides PSPACE-complete tableaux decision procedure