Function-Arity Function

A Function-Arity Function is a function that maps a Function to the Integer Value representing the Number of Function Arguments in the Function.

• See: Cardinality, Conceptual Graph, Concept, Relation, Conceptual Relation Type.

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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 Conceptual Graph with respect to a canon is a tuple G=(C,R, type, referent, arg₁, ..., arg_m), where
    • [math]\displaystyle{ C }[/math] is the set of concepts ; type [math]\displaystyle{ C }[/math] → [math]\displaystyle{ T }[/math] indicates the type of a concept, and referent [math]\displaystyle{ C }[/math] → $I$ indicates the referent marker of a concept.
    • [math]\displaystyle{ R }[/math] is the set of conceptual relations, type [math]\displaystyle{ R }[/math] → [math]\displaystyle{ T }[/math] indicates the type of relation, and each argi [math]\displaystyle{ R }[/math] → [math]\displaystyle{ C }[/math] is a partial function where arg_i(r) indicates the i-th argument of the relation r. The argument functions are partial as they are undefined for arguments higher than the relation’s ‘arity’. We adopt the convention that arg₀ indicates the (at most) one incoming arc. If there is no incoming arc to the relation, then arg₀ is undefined. We also define the function arity(r) which returns an integer value representing the number of arguments that the relation [math]\displaystyle{ r }[/math] has.

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