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Writing a contract with a specific content is a ground for purchase, purchase is a ground for ownership, ownership is a ground for power to dispose. Also power to dispose is a consequence of ownership, ownership is a consequence of purchase, etc. The paper presents a continuation of the authors' previous work on the algebraic representation of ground-consequence chains in normative systems. The paper analyzes different kinds of "implicative closeness" between grounds and consequences in chains of legal concepts, in particular combinations of "weakest ground". "strongest consequence" and "minimal joining". The idea of a concept's being intermediate between concepts of two different sorts is captured by the technical notion of "intervenient", defined in terms of weakest ground and strongest consequence. Lattice theory is used for studying the links between different strata and the structure of intervenient strata. We focus on (1) intervenient minimality, (2) conjunctions and disjunctions of intervenients, (3) organic wholes of intervenients, and (4) a typology of different kinds of intervenients. Also (5), we pay attention to the properties of intervenients in a network of "strata". A legal example concerning grounds and consequences of "ownership" and "trust" is used to illustrate the application of the formal theory. (C) 2011 Elsevier B.V. All rights reserved.