Group Knowledge of Hypothetical Values

TL;DR

This paper develops a comprehensive logical framework for modeling and reasoning about group knowledge of hypothetical variable values during data exchange events, incorporating new operators for distributed and common knowledge under conditions.

Contribution

It introduces novel operators for distributed and common knowledge of hypothetical values, providing a complete axiomatization and decidability results for the logic.

Findings

Complete axiomatization of the logic with data exchange and hypothetical knowledge.

Decidability of the extended logic.

Examples illustrating the logic's application.

Abstract

In recent years, epistemic logics have been extended with operators K_ax 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_ax, one needs to extend the logic further: first, with an operator for distributed knowledge K_Ax of the value (by a group of agents A); next, with a conditional version of this: distributed knowledge K^P_A x (of the value by a group) given some hypothetical condition (expressed by some proposition P); then, with definite descriptions x^P_A , denoting the 'hypothetical' value of x according to A's (distributed) knowledge given condition P. 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.