Base Template InstanceOfRelation

This is a template for expressing relationships that do not have a predefined ISO 15exists 26-2 type.
InstanceOfRelation(a, b, c) means that a is a custom-defined relation by which b is related to c.

1 hasRelation ClassOfRelationshipWithSignature
2 hasFirstElement Thing
3 hasSecondElement Thing


InstanceOfRelation(x1, x2, x3) <-> 
ClassOfRelationshipWithSignature(x1) & 
Thing(x2) & 
Thing(x3) & 
exists u(OtherRelationshipTriple(u, x2, x3) & 
ClassificationOfRelationship(u, x1)) . 

NOTE This template uses the template ClassificationOfRelationship. Where the latter template takes an ordered pair (a relationship) as a single argument to be classified by a relation, this template takes the elements of the ordered pair themselves as arguments. The composition of these elements into an ordered pair is given by the template axiom.

EXAMPLE Let Alfred and ACME Co. be instances of Person, and Employment a custom-defined relation (i.e., a ClassOfRelationshipWithSignature).

Note that — no designation for the classified ordered pair is defined, — the definition of the ClassOfRelationshipWithSignature, which should include specification of roles for the ends of the relation, is not given in the template statement.

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