Definition
Predicate
A predicate in first-order logic is a
symbol that denotes a property or relation applied to objects int he domain
of discourse, which is often called the universe. When given specific inputs
(objects, terms), a predicate evaluates to a truth value
(true or false).
Predicate vs Function
An first-order logic, functions and predicates
serve different roles. A function always maps a set of
objects from the domain to another object in the same domain.
A predicate, however, represents a property or relation and returns a truth value (true or false) when applied to objects. Essentially, functions produce domain elements,
whereas predicates produce truth values.