Virtual Group Knowledge and Group Belief in Topological Evidence Models (Extended Version)
This work addresses foundational issues in formal epistemology and multi-agent systems, providing rigorous logical frameworks for modeling group-level epistemic states, which is incremental but essential for theoretical advancements in the field.
The paper tackles the problem of formalizing group knowledge and belief within multi-agent evidence models by extending topological semantics from individuals to groups, resulting in complete axiomatizations and decidability proofs for these logics, including dynamic extensions with evidence-sharing operators.
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.