Predicate

https://en.wikipedia.org/wiki/Predicate_(mathematical_logic)

A predicate is the formalization of the mathematical concept of statement. A statement is commonly understood as an assertion (declaration) with a truth value (true or false), depending on the values of its constituent variables.

A predicate is a wff that can be evaluated to true or false in function of the values of the variables that occur in it. It can thus be considered as a Boolean-valued function.

A predicate consists of atomic formulas connected with logical connectives.

An atomic formula is a wff of some mathematical theory.

The main logical connectives are

• negation (not or ¬)

• logical conjunction (and or ∧)

• logical disjunction (or or ∨)

• existential quantification (∃)

• universal quantification (∀)

• the predicate 'always true', denoted true or ⟙

• the predicate 'always false', denoted false or ⟘

The last two are commonly considered also as logical connectives.

A predicate without quantifiers is called a propositional formula.

A predicate whose quantifiers all apply to individual elements, and not to sets or predicates, is called a first-order predicate. That is, in FOL predicates range over individuals only, and in HOL over other predicates.