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.

翻译：近年来，认知逻辑已扩展了用于表示（智能体a对）变量x（值）知识的算子K_ax。我们研究了这些逻辑的动态版本，并丰富了用于半公开数据交换事件（例如，公开宣告、子组内数据共享或变量值更改）的模态。为了在存在等式x = y和K_ax的情况下获得数据交换事件的完整公理化，需要进一步扩展逻辑：首先，添加用于表示（群体A的）值分布式知识K_Ax的算子；其次，引入其条件版本：在给定某些假设条件（由命题P表达）下，群体的分布式知识K^P_A x；然后，引入确定描述x^P_A，表示根据A在条件P下的（分布式）知识所得的x的‘假设’值。为了处理半公开数据交换下的共同知识，我们还需要添加一种新颖的条件版本，基于近期提出的共同分布式知识概念。我们研究了所得逻辑，给出示例，并提出了完整的公理化体系及可判定性证明。