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1. Hierarchical relations

In section 3.1.3, we introduced the  composition of modules:  elementary modules can be composed into complex modules, which in their turn can be composed into higher-level complex modules. This hierarchy of composed modules entails asymmetric `hierarchical relations': a complex module contains its constituent modules and, vice versa, these components are part of a complex module.

Hierarchical relations can be defined in any model that allows for  composites of modules, or generally, composites of units. Conklin [Conklin, 1987] encodes more elaborate hierarchical information, with next-siblings, for example, and first-children, first-grandchildren. We distinguish in the ``family tree" only hierarchical relations between ancestors and descendants in general, i.e. constituent modules which are part of the complex modules that contain them. Sibling relations are not expressed in terms of a hierarchy, but in a `proximity-based relation'.

   
[To the full figure] Figure 4.9: Hierarchical, proximity-based and range-based relations: between elementary module E and complex module C there is a ``child-parent" hierarchical relation. Higher-level ``ancestors" of E include the article A, project P and the journal. Between the microscopic E and the mesoscopic module M, there is a range-based relation that expresses the fact that M has a wider range, as well as a proximity-based relation that expresses the fact that they are part of the same project P. Between the elementary module E and complex module C' (as well as article A' and project P') there is neither a hierarchical relation, nor a range-based relation. Still, C', A' and P' all are ``distant cousins" of E according to the proximity-based relation: they are published in the same journal. The mesoscopic M is related by the same range-based relation to E' as to E, but the proximity-based relation between M and E' is weaker: they are only part of the same journal


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