 There are many possible structures of covariation that have been called supervenience theses in the metaphysics literature. For our purposes, it will be convenient to distinguish four of the most influential formulations. (The literature on supervenience contains several other variations; see the entry on  supervenience  for an excellent introduction, from which this entry adopts some of the formulations below. That entry also has very helpful discussion of the contrast between supervenience and certain other metaphysical relations with which it is often associated. The contrast between supervenience and the closely-related notion of entailment, discussed in section 3.2 of the entry on  supervenience,  is especially germane to the topic of this subsection.)