The conventional approach to the general Partial Information Decomposition (PID) problem has been redundancy-based: specifying a measure of redundant information between collections of source variables induces a PID via Moebius-Inversion over the so called redundancy lattice. Despite the prevalence of this method, there has been ongoing interest in examining the problem through the lens of different base-concepts of information, such as synergy, unique information, or union information. Yet, a comprehensive understanding of the logical organization of these different based-concepts and their associated PIDs remains elusive. In this work, we apply the mereological formulation of PID that we introduced in a recent paper to shed light on this problem. Within the mereological approach base-concepts can be expressed in terms of conditions phrased in formal logic on the specific parthood relations between the PID components and the different mutual information terms. We set forth a general pattern of these logical conditions of which all PID base-concepts in the literature are special cases and that also reveals novel base-concepts, in particular a concept we call "vulnerable information".

翻译：针对一般部分信息分解（PID）问题的传统方法基于冗余性：通过指定源变量集合之间的冗余信息度量，利用莫比乌斯反演在所谓的冗余格上诱导出PID。尽管该方法占据主导地位，但学界持续关注从不同基础信息概念（如协同信息、独特信息或并集信息）的视角审视该问题。然而，这些不同基础概念及其关联PID的逻辑组织仍缺乏全面理解。本研究应用我们近期论文中引入的PID分体论表述来阐明该问题。在分体论框架中，基础概念可通过形式逻辑条件加以表达，这些条件描述了PID分量与不同互信息项之间的特定部分-整体关系。我们建立了此类逻辑条件的一般范式，文献中所有PID基础概念均是其特例，并由此揭示了新的基础概念，特别是我们称之为“脆弱信息”的概念。