A predicate is a statement or mathematical assertion that contains variables, sometimes referred to as predicate variables, and may be true or false depending on those variables’ value or values. • In
propositional logic,
atomic formulas are sometimes regarded as zero-place predicates. In a sense, these are nullary (i.e. 0-
arity) predicates. • In
first-order logic, a predicate is a
non-logical relation symbol, which forms an atomic formula when applied to an appropriate number of
terms. • In
set theory with the
law of excluded middle, predicates are understood to be
characteristic functions or set
indicator functions (i.e.,
functions from a set element to a
truth value).
Set-builder notation makes use of predicates to define sets. • In
autoepistemic logic, which rejects the law of excluded middle, predicates may be true, false, or simply
unknown. In particular, a given collection of facts may be insufficient to determine the truth or falsehood of a predicate. • In
fuzzy logic, the strict true/false valuation of the predicate is replaced by a quantity interpreted as the degree of truth. ==See also==