(a) & (b) & (c) & (d)

Here you will practice the inference of the Wumpus world using first-order logic.

(a) For the following rules of the Wumpus world, rewrite them into FOL sentences. You can use Breezy, Smelly, Pit, Safe, At, and Adjacent as the predicates. (Adjacent is a relation between two squares. At is a relation between an object and a square. Treat Wumpus as a constant object.)

A square with no Wumpus and no pit is safe. (This is the definition of the predicate Safe.) A square adjacent to a pit is breezy. A square adjacent to the Wumpus is smelly. The Wumpus can only be in a square with no pit. The square (1,1) is safe. (b) Let the KB contain the sentences in (a). Convert them to conjunctive normal form. (c) Given the following facts: The square (1,1) is not breezy.The square (1,1) is not smelly. Use generalized resolution to prove that the square (2,1) is safe. Indicate all the substitutions. (d) Given the following additional facts: The square (2,1) is breezy and smelly. The square (1,2) is smelly and not breezy. Use generalized resolution to prove that the Wumpus is at square (2,2). Indicate all the substitutions.