# Relation Type

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A Relation Type is a type that can be associated with a relation instance.

**Context:**- It can be a Set Member of a Relation Type Set.

**Examples(s):**- an Is-A Relation.

**See:**Ontology, Conceptual Graph Theory, Canon, Type Set, Individual, Subtype Relation, Conformity Relation, Canonical Basis Function.

## References

### 2008

- (Corbett, 2008) ⇒ Dan R. Corbett. (2008). “Graph-based Representation and Reasoning for Ontologies.” In: Studies in Computational Intelligence, Springer. [http://dx.doi.org/10.1007/978-3-540-78293-3 10.1007/978-3-540-78293-3 doi:[http://dx.doi.org/10.1007/978-3-540-78293-3 10.1007/978-3-540-78293-3)
- QUOTE: A canon is a tuple (
*T, I*, =, ::,*B*), where- [math]\displaystyle{ T }[/math] is the set of
*types*; we will further assume that [math]\displaystyle{ T }[/math] contains two disjunctive subsets*T*and T_{C}_{R}containing types for concepts and relations. - $I$ is the set of
*individuals*. - ≤ ⊆
*T*×*T*is the subtype relation*. It is assumed to be a lattice (so there are types*`T`

and ⊥ and operations ∧ and ∨). - :: ⊂
*I*×*T*is the conformity relation*. The conformity relation relates type labels to individual markers; this is essentially the relation which ensures that the typing of the concepts makes sense in the domain, and helps to enforce the type hierarchy.* - [math]\displaystyle{ B }[/math] is the
*Canonical Basis function*(also called s in the Conceptual Graphs literature). This function associates each relation type with the concept types that may be used with that relation; this helps to guarantee well-formed graphs.

- [math]\displaystyle{ T }[/math] is the set of
- …
- QUOTE: An ontology in a given domain [math]\displaystyle{ M }[/math] with respect to a canon is a tuple (
*T*), where_{CM}, T_{RM}, I_{M}*T*is the set of concept types for the domain [math]\displaystyle{ M }[/math] and T_{CM}_{RM}is the set of relation types for the domain*M*.- "
*I*is the set of individuals for the domain_{M}*M*.

- …
- Given two relation types, [math]\displaystyle{ s }[/math] and
*t, s*is said to have a projection into [math]\displaystyle{ t }[/math] if and only if there is a morphism*h*: [math]\displaystyle{ R }[/math] → [math]\displaystyle{ R }[/math], such that: ∀r_{R}*∈ [math]\displaystyle{ R }[/math] and ∀*r*∈ [math]\displaystyle{ R }[/math], hR(r) = r only if type(*r*) ≥ type'(*r) [math]\displaystyle{ R }[/math] is the set of relations, and*type*: [math]\displaystyle{ R }[/math] → [math]\displaystyle{ T }[/math] indicates the type of a relation.

- QUOTE: A canon is a tuple (