Editing Hierarchy (section)

===Containment hierarchy===
[[File:Containment Hierarchy example.png|300px|thumb|right|A diagram illustrating a containment hierarchy. The set of all squares is completely contained in the larger set of quadrilaterals, and so on.]]
A containment hierarchy is a direct extrapolation of the [[#Nested hierarchy|nested hierarchy]] concept. All of the ordered sets are still nested, but every set must be "[[strict subset|strict]]"—no two sets can be identical. The shapes example above can be modified to demonstrate this:

: <math> \text{square} \subsetneq \text{quadrilateral} \subsetneq \text{polygon} \subsetneq \text{shape} \, </math>

The notation <math> x \subsetneq y \, </math> means ''x'' is a subset of ''y'' but is not equal to&nbsp;''y''.

A general example of a containment hierarchy is demonstrated in [[inheritance (object-oriented programming)|class inheritance]] in [[object-oriented programming]].

Two types of containment hierarchies are the ''subsumptive'' containment hierarchy and the ''compositional'' containment hierarchy. A subsumptive hierarchy "[[wikt:subsume|subsumes]]" its children, and a compositional hierarchy is "[[wikt:composed|composed]]" of its children. A hierarchy can also be both subsumptive ''and'' compositional{{example needed|date=August 2018}}.<ref name="AI industrial">{{cite encyclopedia|title=Industrial and Engineering Applications of Artificial Intelligence and Expert Systems|last1=Kopisch|first1=Manfred|last2=Günther|first2=Andreas|doi=10.1007/BFb0024994|editor-last=Belli|editor-first=Fevzi|encyclopedia=Industrial and engineering applications of artificial intelligence and expert systems: 5th international conference, IEA/AIE-92, Paderborn, Germany, June 9–12, 1992 : proceedings|year=1992|publisher=[[Springer Science+Business Media|Springer]]|pages=424–427|isbn=3-540-55601-X|series=Lecture Notes in Computer Science Series|volume=602|issn=0302-9743|editor6-last=Radermacher|editor8-first=Franz-Josef|chapter=Configuration of a passenger aircraft cabin based on conceptual hierarchy, constraints and flexible control}}</ref>