| | 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. |
