I am working my way through this paper on Bayesian Hierarchical Clustering. I keep seeing the phrase tree-consistent. However, it doesn't seem to be defined anywhere in the paper. There is a description of the concept in figure 1.b, but it isn't a formal definition really. I have looked in other papers on the topic referencing the idea of tree-consistency and noticed that they don't formally define the concept either. Although I may be overlooking a paper on the topic.
Does anyone know of a formal definition for this?