hierarchy
the basic structural principle according to which elements of a set are ordered. The graphic representation of a hierarchy furnishes a tree diagram which branches downwards. Hierarchies may be specified as follows: a two-placed relation R is a hierarchy if and only if the following five conditions are met: (a) there is a point of origin; (b) all elements are connected to this point of origin; (c) there is no upward branching; (d) R is asymmetric (symmetric relation); (e) R is transitive (transitive relation). Hierarchies have a broad range of applications from taxonomic classifications of the human environment to dominance relations in society. In linguistics, hierarchies exist in syntax, in lexical semantics, and in markedness theory.