Containment hierarchy
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A containment hierarchy is a hierarchical collection of strictly nested sets. Each entry in the hierarchy designates a set of which the previous entry is a strict superset, and the next entry is a strict subset. For example, all rectangles are quadrilaterals, but not all quadrilaterals are rectangles, and all squares are rectangles, but not all rectangles are squares. A hierarchy of this kind is to be contrasted with a more general notion of a partially ordered set.
A taxonomy is a classic example of a containment hierarchy.
Examples
- Geometry
- shape → polygon → quadrilateral → rectangle → square
- Particle physics
- particle → elementary particle → fermion → lepton → electron
- Philosophy
- abstract → concept → idea → application → concrete
- Biology
- Biological classification: animal → bird → raptor → eagle → golden eagle
- Hierarchy of life: organism → organ system → organ → tissue → cell
- Formal grammars
- Chomsky hierarchy: unrestricted → context-sensitive → context-free → regular
See also
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