Translating English to FOL
- Every gardener likes the sun.
(∀x) gardener(x) ⇒ likes(x,Sun)
- You can fool some of the people all of the time.
(∃x)(∀t) (person(x) ∧ time(t)) ⇒ can-fool(x,t)
- You can fool all of the people some of the time.
(∀x)(∃t) (person(x) ∧ time(t) ⇒ can-fool(x,t)
- All purple mushrooms are poisonous.
(∀x) (mushroom(x) ∧ purple(x)) ⇒ poisonous(x)
- No purple mushroom is poisonous.
¬(∃x) purple(x) ∧ mushroom(x) ∧ poisonous(x)
or, equivalently,
(∀x) (mushroom(x) ∧ purple(x)) ⇒ ¬poisonous(x)
- There are exactly two purple mushrooms.
(∃x)(∃y) mushroom(x) ∧ purple(x) ∧ mushroom(y) ∧ purple(y) ∧
¬(x=y) ∧ (∀z) (mushroom(z) ∧ purple(z)) ⇒ ((x=z) ∨ (y=z))
- Deb is not tall.
¬tall(Deb)
- X is above Y if X is on directly on top of Y or else there is
a pile of one or more other objects directly on top of one another
starting with X and ending with Y.
(∀x)(∀y) above(x,y) ⇒ (on(x,y) ∨ (∃z) (on(x,z) ∧ above(z,y)))