Relation Type

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



  • (Corbett, 2008) ⇒ Dan R. Corbett. (2008). “Graph-based Representation and Reasoning for Ontologies.” In: Studies in Computational Intelligence, Springer. [ 10.1007/978-3-540-78293-3 doi:[ 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 TC and TR 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 (TCM, TRM, IM), where
      • TCM is the set of concept types for the domain [math]\displaystyle{ M }[/math] and TRM is the set of relation types for the domain M.
      • "IM 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 hR : [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.