Exercise 5        Name __________________        Score __/6

1. Let S_i,j be true when square [i,j] is smelly.

   Let W_i,j be true when square [i,j] is the wumpus.

   The agent is in [1,1]

   • What sentences, in terms of W and S, are in the KB for the relevant squares? Include the percepts.
     
     W_1,1
     S_1,1
     S_1,1(W_1,2W_2,1)       
      

   The agent moves to square [1,2].

   • What sentences, in terms of W and S, are included in the KB for the relevant squares? Include the percepts. 

     W_1,1
     W_1,2
     S_1,1
     S_1,2
     S_1,1(W_1,2W_2,1)       
     S_1,2(W_1,1W_2,2W_3,1)
      

2. Prove W_2,1

   S_1,1(W_1,2W_2,1)      biconditional elimination
         (S_1,1(W_1,2W_2,1))((W_1,2W_2,1)S_1,1)
   ((W_1,2W_2,1)S_1,1)        And reduction
   (S_1,1(W_1,2W_2,1))   Contraposition
   (W_1,2W_2,1)                  Modus Ponens and percept S_1,1
   W_1,2W_2,1                   de Morgan
   W_2,1                               And reduction