Group Knowledge of Hypothetical Values
Alexandru Baltag, Sonja Smets · Electronic Proceedings in Theoretical Computer Science · 2025
In recent years, epistemic logics have been extended with operators K a x for knowledge of (the value of) a variable x (by an agent a).We study dynamic versions of these logics, enriched with modalities for semi-public data-exchange events (e.g., public announcements, data-sharing within a subgroup, or changing the value of a variable).To obtain a complete axiomatization of data-exchange events, in the presence of equality x = y and K a x, one needs to extend the logic further: first, with an operator for distributed knowledge K A x of the value (by a group of agents A); next, with a conditional version of this: distributed knowledge K ϕ A x (of the value by a group) given some hypothetical condition (expressed by some proposition ϕ); then, with definite descriptions x ϕ A , denoting the 'hypothetical' value of x according to A's (distributed) knowledge given condition ϕ.In order to deal with common knowledge in the presence of semi-public data exchanges, we also need to add a novel conditional version of the recent concept of common distributed knowledge.We investigate the resulting logic, giving examples and presenting a complete axiomatization and a decidability proof.