Type Set

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A Type Set is a set of Types.



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]T[/math] is the set of types ; we will further assume that [math]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]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.