In this problem, we will use 1st order logic to represent and reason with knowledge about the wumpus world.
In this problem, you will show that the following assertions (A1), (A2), (A3), and (A4) together entail (C) by constructing a proof by refulation using resolution.
- (A1). Every edible mushroom or poisonous mushroom is a mushroom.
∀x [Edible(x) ∨ Poisonous(x) ⇒ Mushroom(x)]
- (A2). Every mushroom is grey, white, or yellow.
∀y [Mushroom(y) ⇒ Grey(y) ∨ White(y) ∨ Yellow(y)]
- (A3). No edible mushroom is yellow.
∀z [Edible(z) ⇒ ¬ Yellow(z)]
- (A4). No mushroom that is organic is grey.
∀w [Mushroom(w) ∧ Organic(w) ⇒ ¬ Grey(w)]
- (C). If no mushroom is white, then no edible mushroom is organic.
[∀i [Mushroom(i) ⇒ ¬ White(i)]] ⇒ [¬∃j [Edible (j) ∧ Organic(j)]]