Base Templates SpecializationAsEnd1UniversalRestriction, SpecializationAsEnd2UniversalRestriction


SpecializationAsEnd1UniversalRestriction and SpecializationAsEnd2UniversalRestriction are templates for expressing relation specialisations with the force of universal restriction. These templates have the same roles, and similar definitions except for the use of reference items End1UniversalRestriction, resp. !End2UniversalRestriction.

SpecializationAsEnd1UniversalRestriction means that a and b are relations, that a is a subrelation of b, and that the specialization relation between a and b is a member of End1UniversalRestriction.

Roles:
1 hasSubrelation ClassOfRelationship
2 hasSuperrelation ClassOfRelationship

Axiom:

SpecializationAsEnd1UniversalRestriction(x1, x2) <-> 
ClassOfRelationship(x1) & 
ClassOfRelationship(x2) & 
exists y(SpecializationTriple(y, x1, x2)& 
ClassificationTemplate(y, End1UniversalRestriction)) 

Axiom:

SpecializationAsEnd2UniversalRestriction(x1, x2) <-> 
ClassOfRelationship(x1) & 
ClassOfRelationship(x2) & 
exists y(SpecializationTriple(y, x1, x2)& 
ClassificationTemplate(y, End2UniversalRestriction)) . 

NOTE A statement SpecializationAsEnd1UniversalRestriction(a, b) implies that the specialization 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.

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