Predicate Logic

★★★☆☆High School

📖Definition

Predicate logic (first-order logic) extends propositional logic with variables, quantifiers (∀, ∃), and predicates. It can express mathematical statements precisely.

📐Formulas

∀ x P(x)

Universal quantifier (for all x)

∃ x P(x)

Existential quantifier (there exists x)

¬ (∀ x P(x)) ≡ ∃ x ¬ P(x)

Quantifier negation

✏️Examples

예제 1

Express 'All humans are mortal' in predicate logic.

예제 2

Express 'For every natural number, there's a larger prime'.

Applications

Mathematics

Axiomatic systems, theorem proving

AI

Automated theorem proving, knowledge bases

Databases

Theoretical foundation of SQL

🔗Related Documents

Prerequisites

Related

#술어#양화사#predicate#quantifier