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：针对一般性部分信息分解（PID）问题的传统方法基于冗余性：通过指定源变量集合间的冗余信息度量，利用莫比乌斯反演在所谓的冗余格上推导出PID。尽管该方法普遍存在，但学界持续关注从不同基础信息概念（如协同信息、独特信息或联合信息）的视角审视该问题。然而，对这些不同基础概念及其相关PID的逻辑组织方式的全面理解仍不明确。本文运用我们近期提出的PID分体论表述来阐明这一问题。在分体论框架下，基础概念可通过形式逻辑中关于PID组成部分与不同互信息项之间特定部分关系的条件加以表达。我们提出了这些逻辑条件的一般模式，文献中所有PID基础概念均为其特例，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。