gen-define-first-order-logic-and-give-one-short-worked-example-b1c6

Define first-order logic and give one short worked example.

# First-Order Logic **First-order logic (FOL)** is a formal system for expressing statements about objects, their properties, and relationships. It extends propositional logic by adding: - **Variables**: x, y, z (ranging over objects in a domain) - **Predicates**: P(x), Equal(x,y) (properties and relations) - **Quantifiers**: - ∀ (universal: "for all") - ∃ (existential: "there exists") - **Functions**: f(x), plus(x,y) (map objects to objects) ## Worked Example **English statement**: "Every student has a favorite professor." **Translation to FOL**: ``` ∀x (Student(x) → ∃y (Professor(y) ∧ FavoriteProfessor(x,y))) ``` **Reading it back**: - ∀x: "For all x" - Student(x) →: "if x is a student, then" - ∃y: "there exists some y such that" - Professor(y) ∧ FavoriteProfessor(x,y): "y is a professor AND y is x's favorite professor" **Evaluation**: This formula is true in a domain if and only if we can find, for each student, at least one professor who is their favorite.