Arity is a term that is occasionally used to refer to much the same as valency (e.g. Reinhart & Siloni 2005) and refers to the number of arguments that a predicate takes. The predicate P in the formula P(a,b) has arity 2 (is a two-place predicate) because it takes two arguments a and b. Generally, a predicate with arity n is called an n-place predicate. Another term for arity is adicity.
The term was taken from mathematics. According to the OED, arity is "the number of elements by virtue of which something is unary, binary, etc."
- Gamut, L.T.F. 1991. Logic, language, and meaning, Univ. of Chicago Press, Chicago.
- Reinhart, Tanya & Siloni, Tal. 2005. "The lexicon-syntax parameter: reflexivization and other arity operations." Linguistic Inquiry 36.3:389-436.