Foundations of Semantic Web Technologies

OWL Formal Semantics 169

We give an example of a role hierarchy which is not regular:

hasParent ◦ hasHusband v hasFather

hasFather v hasParent

This role hierarchy is not regular because regularity would enforce both

hasParent ≺ hasFather and hasFather ≺ hasParent, which is impossi-

ble because ≺ must be strict.

Note that regular role hierarchies must not contain role equivalences: If we

had R v S and S v R, then regularity would enforce R ≺ S and S ≺ R, which

is impossible because ≺ must be strict. Formally, however, this restriction

is not severe, since it basically means that we do not allow roles to have

synonyms, i.e. if a knowledge base would contain ...