We introduce an extension of the partitioned local depth (PaLD) algorithm that is adapted to online applications such as semi-supervised prediction. The new algorithm we present, online PaLD, is well-suited to situations where it is a possible to pre-compute a cohesion network from a reference dataset. After $O(n^3)$ steps to construct a queryable data structure, online PaLD can extend the cohesion network to a new data point in $O(n^2)$ time. Our approach complements previous speed up approaches based on approximation and parallelism. For illustrations, we present applications to online anomaly detection and semi-supervised classification for health-care datasets.

We propose a structure to represent the social fabric of a group. We call it the `cohesion network' of the group. It can be seen as a graph whose vertices are strict subgroups and whose edges indicate a prescribed `pro-social behaviour' from one subgroup towards another. In social psychology, pro-social behaviours are building blocks of full-blown cooperation, which we assimilate here with `group cohesiveness'. We then define a formal framework to study cohesive group agency. To do so, we simply instantiate pro-social behaviour with the more specific relation of `successful assistance' between acting entities in a group. The relations of assistance within a group at the moment of agency constitute the social fabric of the cohesive group agency. We build our logical theory upon the logic of agency "bringing-it-about". We obtain a family of logics of cohesive group agency, one for every class of cohesion networks.

In this paper we provide a generalization of the concept of cohesion as introduced recently by Berenhaut, Moore and Melvin [Proceedings of the National Academy of Sciences, 119 (4) (2022)]. The formulation presented builds on the technique of partitioned local depth by distilling two key probabilistic concepts: local relevance and support division. Earlier results are extended within the new context, and examples of applications to revealing communities in data with uncertainty are included. The work sheds light on the foundations of partitioned local depth, and extends the original ideas to enable probabilistic consideration of uncertain, variable and potentially conflicting information.