Definitions

from Wiktionary, Creative Commons Attribution/Share-Alike License

  • n. The number of arguments or operands a function or operation takes. For a relation, the number of domains in the corresponding Cartesian product.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

  • n. the number of arguments that a function can take

Etymologies

From -ary, based on a Latin root. Compare adicity and adinity, based on the corresponding Greek root. (Wiktionary)

Examples

  • r is called the arity of the function f, i.e., the number of arguments that it takes.

    Computability and Complexity

  • Then due to its popul­arity, the dates were extended twice until the end of August.

    20th Century German Art Exhibition, London 1938

  • A structure contains interpretations of certain predicate, function and constant symbols; each predicate or function symbol has a fixed arity.

    Model Theory

  • A signature is a set of individual constants, predicate symbols and function symbols; each of the predicate symbols and function symbols has an arity

    First-order Model Theory

  • In 1870 Peirce published a long paper “Description of a Notation for the Logic of Relatives” in which he introduced for the first time in history, two years before Frege's Begriffschrift a complete syntax for the logic of relations of arbitrary adicity (or: arity).

    Nobody Knows Nothing

  • Again: rheme (by which Peirce meant a relation of arbitrary adicity or arity) was a first, proposition was a second, and argument was a third.

    Nobody Knows Nothing

  • These axioms tacitly specify the arity of a combinator as well as their reduction (or contraction) pattern.

    Combinatory Logic

  • P and Q (or for predicates of higher arity when the variable in their last argument is bound).

    Combinatory Logic

  • Predicates have a fixed finite arity in FOL, and nothing precludes binding at once a variable in the first argument of one predicate and in the second argument of another predicate.

    Combinatory Logic

  • Primitive recursion: if f and g are primitive recursive functions of arity k and k+2, respectively, then there is a primitive recursive function, h, of arity k+1 satisfying the following conditions:

    Computability and Complexity

Comments

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  • the number of arguments that a predicate takes. Generally, a predicate with arity n is called an n-place predicate. Another term for arity is adicity.

    October 14, 2009