Theory of first order logic in Artificial intelligence

• Whereas propositional logic assumes the world contains facts
• First-order logic (like natural language) assumes the world contains
  • Objects: people, houses, numbers, colors, baseball games, wars, …
  • Relations: red, round, prime, brother of, bigger than, part of, comes between, …
  • Functions: father of, best friend, one more than, plus, …

Models for FOL: Example

Example

• Five objects
• Two binary relations
• Three unary relations
• One unary function

Syntax of FOL: Basic Elements

• Basic symbols: objects (constant symbols), relations (predicate symbols), and functions (functional symbols).
• Constants King John, 2, Wumpus…
• Predicates Brother, >,…
• Functions Sqrt, LeftLegOf,…
• Variables x, y, a, b,…