Relation Type

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.

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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_C and T_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.
  • …
  • QUOTE: An ontology in a given domain [math]\displaystyle{ M }[/math] with respect to a canon is a tuple (T_CM, T_RM, I_M), where
    • T_CM is the set of concept types for the domain [math]\displaystyle{ M }[/math] and T_RM is the set of relation types for the domain M.
    • “I_M is the set of individuals for the domain 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_R : [math]\displaystyle{ R }[/math] → [math]\displaystyle{ R }[/math], such that: ∀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.

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