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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
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