Similarity and dissimilarity in posets

The relevance of partially ordered sets (or posets) in a wide diversity of contexts in chemistry is emphasized, and the utility of distance functions (or metrics) on such posets is noted. First a notion of scale similarity is introduced to make comparisons within certain so-called scaled posets, for which there is formulated natural comparators, which in turn lead to associated distance functions. Beyond taking note of several chemically relevant examples of these scaled posets and their consequent associated similarity measures, a second chemically relevant class of so-called shifted posets is similarly developed, with examples. Even further extension of some aspects of the current approach is indicated, and finally the multi-posetic character of chemical periodic law is suggested.