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

## TL;DR

This paper extends topological evidence models to multi-agent groups, axiomatizes the logic of group knowledge and belief, and introduces dynamic evidence-sharing operators with complete axiomatizations.

## Contribution

It provides a complete axiomatization and decidability results for the logic of group evidence, knowledge, and belief, including dynamic sharing extensions.

## Key findings

- Complete axiomatization of group evidence logic
- Decidability of the logic of group knowledge and belief
- Dynamic evidence-sharing operators are co-expressive with static logics

## 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.