| 1 | === Base Templates !SpecializationAsEnd1UniversalRestriction, !SpecializationAsEnd2UniversalRestriction === |

| 2 | |

| 3 | [[br]]!SpecializationAsEnd1UniversalRestriction and !SpecializationAsEnd2UniversalRestriction |

| 4 | are templates for expressing relation specialisations with the force of universal restriction. |

| 5 | These templates have the same roles, and similar definitions except for the use of reference |

| 6 | items !End1UniversalRestriction, resp. !End2UniversalRestriction. |

| 7 | [[br]] |

| 8 | [[br]]!SpecializationAsEnd1UniversalRestriction means that a and b are relations, that a is a |

| 9 | subrelation of b, and that the specialization relation between a and b is a member of |

| 10 | End1UniversalRestriction. |

| 11 | [[br]] |

| 12 | [[br]]Roles: |

| 13 | [[br]]1 hasSubrelation !ClassOfRelationship |

| 14 | [[br]]2 hasSuperrelation !ClassOfRelationship |

| 15 | |

| 16 | Axiom: |

| 17 | {{{ |

| 18 | SpecializationAsEnd1UniversalRestriction(x1, x2) <-> |

| 19 | ClassOfRelationship(x1) & |

| 20 | ClassOfRelationship(x2) & |

| 21 | exists y(SpecializationTriple(y, x1, x2)& |

| 22 | ClassificationTemplate(y, End1UniversalRestriction)) |

| 23 | }}} |

| 24 | Axiom: |

| 25 | {{{ |

| 26 | SpecializationAsEnd2UniversalRestriction(x1, x2) <-> |

| 27 | ClassOfRelationship(x1) & |

| 28 | ClassOfRelationship(x2) & |

| 29 | exists y(SpecializationTriple(y, x1, x2)& |

| 30 | ClassificationTemplate(y, End2UniversalRestriction)) . |

| 31 | }}} |

| 32 | |

| 33 | NOTE A statement !SpecializationAsEnd1UniversalRestriction(a, b) implies that the specialization |

| 34 | of b to a has the force of a universal restriction on the class that is the domain of a: any pair in b for which the first element is a member of the domain of a is a member of a. (Accordingly, !SpecializationAsEnd2UniversalRestriction(a, b) constrains the range of a). See 8.4 for further information on the representation used in this template. |