What is a Predicate?

“A predicate is a statement with blanks that become true or false when we fill them in.” More formally, a predicate is a symbol that represents a relation. P(a) is an atomic formula, where P is the predicate, and a is “filled” in P the predicate, hence creating a logical formula.

Example, P is a predicate symbol, > is a predicate symbol, but ‘x > 0’ is a predicate.

Predicates are a fundamental notion in first-(and higher)-order-logic, because they let us open up the atoms, peer inside them. This isn’t the case with propositional logic, over there atoms can not be peered inside, ‘p’ and ‘q’ stand for whole propositions, i.e., the atoms are indivisible. Although compound formulae/propositions such as ‘p ∧ q’ are fine for inspection.