WUMPUS WORLD and Propositional Logic



 
 

1, 4
 
 
 

 

 2, 4 3, 4 4, 4
1, 3
 
 
 

 

 2, 3 3, 3 4, 3
1, 2

AGENT
Stench
OK


 2, 2
 
 

OK

 3, 2 4, 2
1, 1
 
 

VISITED
OK

 2, 1
 
 

Breeze
VISITED
OK




 

 3, 1
 
 

PIT

 4, 1

        "Percept" Sentences in KB :

                ! S1,1                                    ! B1,1
                ! S2,1                                      B2,1
                  S1,2                                    ! B1,2
 

        "Knowledge about the Environment" Sentences in KB :
        ("If no stench in...")

       R1 :    ! S1,1 ==>  ! W1,1   &    ! W1,2    &    ! W2,1
        R2 :    ! S2,1 ==>  ! W1,1   &    ! W2,1   &    ! W2,2     &    ! W3,1
        R3 :    ! S1,2 ==>  ! W1,1   &    ! W1,2    &    ! W2,2      &    ! W1,3

        ("If stench in ...")
       R4 :      S1,2 ==>    W1,3    ||       W1,2    ||        W2,2      ||       W1,1
 

        FINDING THE WUMPUS :

        1. (MP) to R1 derives :
              ! W1,1   &    ! W1,2    &    ! W2,1
        2. (AE) to 1. derives :
              ! W1,1          ! W1,2           ! W2,1
        3. (MP) to R2 derives :
              ! W1,1   &    ! W2,1   &    ! W2,2     &    ! W3,1
        4. (AE) to 3. derives :
              ! W1,1          ! W2,1           ! W2,2             ! W3,1
        5. (MP) to R4 derives :
              W1,3    ||       W1,2    ||        W2,2      ||       W1,1
        6. (UR) to 5. (W1,3    ||       W1,2    ||        W2,2      ||       W1,1) and 2. (!W1,1) derives :
              W1,3    ||       W1,2    ||        W2,2
        7. (UR) to 6. (W1,3    ||       W1,2    ||        W2,2) and 4. (! W2,2) derives :
              W1,3    ||       W1,2
        8. (UR) to 7. (W1,3    ||       W1,2) and 2. (! W1,2) derives :
              W1,3.

    Thus, WUMPUS is in the cell 1,3 !!!! Watch out.
 
 

        "Translating Knowledge into Action" Sentences in KB :

       A1,1   &    East      &    W2,1         ==>       ! Forward
 

        Problems with PROPOSITIONAL AGENT :

        (i)    TOO MANY RULES
                (to state "don't go forward if the wumpus is in front of you",
                one needs 16 (# of cells) * 4 (# of orientations) = 64 rules)

        (ii)    HANDLING CHANGE
               (Initially A1,1 is true but once the agent moves somewhere
                else, it becomes false and A1,1 is true. Thus, time needs to
                be represented.)

      A1,10   &    East0      &    W2,10         ==>       ! Forward0
      A1,11   &    East1      &    W2,11         ==>       ! Forward1
      A1,12   &    East2      &    W2,12         ==>       ! Forward2
      ..............................................

        For 100 time steps, one needs 6400 of these rules.

        In first order logic these get replaced by ONE rule :

                "i "j "k  [ Ai,jk   &    Eastk      &    Wi+1,jk         ==>       ! Forwardk  ]