adicity
English
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Etymology
[edit]From -adic (taken from monadic/dyadic/triadic [function/operator]) + -ity, or alternatively from -ad (taken from monad/duad/triad) + -icity. Compare Latinate equivalent arity, based on -ary.
Noun
[edit]adicity (plural adicities)
- (logic, mathematics, computer science) The number of arguments or operands a function or operation takes. For a relation, the number of domains in the corresponding Cartesian product.
- 1997, Robert W. Burch, 13: Peirce's Reduction Thesis, Nathan Houser, Don D. Roberts, James Van Evra (editor), Studies in the Logic of Charles Sanders Peirce, Indiana University Press, page 233,
- Equivalently, it says that all relations of adicity greater than 3 may be reduced to relations of adicities 1, 2, and/or 3. The negative component of the Thesis says, first, that relations of adicity 2 may not in general be constructed from (reduced to) relations exclusively of adicity 1; and, second, that relations of adicity 3 and greater may not in general be constructed from (equivalently: reduced to) relations exclusively of adicities 1 and/or 2.
- 2004, Susan Rothstein, Predicates and Their Subjects, Springer, page 47:
- What can be predicted is that the adicity of any syntactic predicate is the same: since its adicity is a grammatical and not a thematic fact, semantic differences between predicates cannot affect their grammatical structure.
- 2007, Helier J. Robinson, Relation Philosophy of Mathematics, Science, and Mind, Sharebooks Publishing, 2nd Edition, page 68,
- We have seen that every relation, without exception, necessarily has a term set, and the necessary properties of simplicity and an adicity: relations without these are impossible, merely nominal.
- 1997, Robert W. Burch, 13: Peirce's Reduction Thesis, Nathan Houser, Don D. Roberts, James Van Evra (editor), Studies in the Logic of Charles Sanders Peirce, Indiana University Press, page 233,
- (chemistry, obsolete) Valence.
Synonyms
[edit]Related terms
[edit]Translations
[edit]number of arguments