The Universal Quantifier

• ∀ means for all.
• ∀ x (basketballPlayer(x) -> tall(x)) means for all. That is all basketball players are tall.
• This enables you to derive new facts.
• If you find out (basketballPlayer(Ervin)), what new fact can you derive?
• ∀ x (swan(x) -> white(x)) means all swans are white.
• This is the classic example.
• You can have multiple variables in these things.
• ∀ x,y,z (mother(x,y) and mother (y,z) -> grandmother(x,z)).
• This means that for every person x,y, and z where x is the mother of y, and y is the mother of z, you can derive x is the gradmother of z.