Subsumption hierarchies, taxonomies and generalisation

The subsumption relation can be understood as a relation of implication which relates more specific to more general concepts in conceptual taxonomies. In formal terms, subsumption defines a lattice, a kind of partial ordering, which may be represented as a directed acyclic graph. The hierarchical graphs defined by subsumption need not be trees, but can be more general kinds of graph in which child nodes are re-entrant, i.e. a child node may have more than one parent node. However, commonly a subsumption lattice has a core tree structure, with superimposition of more than one tree, or of other cross-classifiying structures. The subsumption relation may be seen as a generalisation relation, in that the subsumer expresses a generalisation over the subsumed.

Examples of lexical subsumption are shown in Figure 1, which illustrates some of the following points:

1.   The semantic properties of horse subsume the semantic properties of stallion.
2.   The semantic properties {male, animal} subsume the semantic properties of stallion
3.   The semantic properties of horse subsume the semantic properties of mare.
4. The phonological properties of lamp subsume the phonological properties of streetlamp
5. Heads subsume the constructions whose heads they are.
6. 
7. Archiphonemes subsume their phoneme members.

 
Figure 1: Reentrant subsumption graphs 

 
Figure 2: Reentrant inheritance graphs