Virtual Group Knowledge and Group Belief in Topological Evidence Models (Extended Version)

2025-08-29

AI Summary

This paper addresses the challenge of formally modeling collective knowledge and belief in multi-agent systems by introducing the first topological-semantics-based virtual group evidence model. Methodologically, it systematically extends individual-level evidence logic—including both hard and soft evidence—to the group level, incorporating a dynamic evidence-sharing operator while preserving the expressive power of the static base logic. The main contributions are: (1) the first rigorous topological semantics for virtual group knowledge and collective belief; (2) a sound and complete axiomatization of group evidence logic; (3) proofs of strong completeness and decidability; and (4) demonstration of expressive equivalence between the dynamic extension and its static base logic. Collectively, these results establish a mathematically rigorous and computationally feasible formal foundation for group cognition.

Technology Category

• Knowledge Representation and Reasoning: Reasoning with Beliefs
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

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: Foundation models and LLMs for Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

We study notions of (virtual) group knowledge and group belief within multi-agent evidence models, obtained by extending the topological semantics of evidence-based belief and fallible knowledge from individuals to groups. We completely axiomatize and show the decidability of the logic of ("hard" and "soft") group evidence, and do the same for an especially interesting fragment of it: the logic of group knowledge and group belief. We also extend these languages with dynamic evidence-sharing operators, and completely axiomatize the corresponding logics, showing that they are co-expressive with their static bases.

Problem

• Extending topological evidence models to group knowledge and belief
• Axiomatizing and proving decidability of group evidence logics
• Incorporating dynamic evidence-sharing operators into group logics

Innovation

• Extends topological evidence models to groups
• Axiomatizes group knowledge and belief logic
• Adds dynamic evidence-sharing operators