2. (4 points) This is the Wumps world problem which has 4 x 4 squares. PIT PIT P
ID: 3604909 • Letter: 2
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2. (4 points) This is the Wumps world problem which has 4 x 4 squares. PIT PIT PIT Let Pij be true if there is a pit in [i,j]. Let Wij be true if there is a wumps in [i,j] Let Bij be true if there is a breeze in [i,j]. Let Sij be true if there is a smell in [i,j]. Pits cause breezes in adjacent squares Wumps cause smells in adjacent squares The given knowledge base is from (1) to (20). This is all you have. You need to convert the necessary followings to CNF and apply inference rules. (2) (B2, 1(P 1,1 v P2,2 v P3, 1 )) (1) (B1,1(P1,2v P2,1)) (3) (B1,2(P1,lv P2,2 v P13)) (4) (B 1,3(P 1,2v P2,3x P 1,4 )) (5) (B3,1 (P2,1v P3,2 v P4,1)) (6) (SI,l (W1,2vW2,1)) (9) (S 1,3(W1,2v W2,3 v W 1,4 )) (10) (S3,l (W2,lv W3,2 v W4,1 )) (11) B1,1 (12)-S1, (13) S2,1 (14) B1,2 (15) B2,1 (16) S1,4 (17) B4,1 (18) S1,2 (19) B3,2 (20) S2,3 (2-1) Method 1: Provethat position3hasawumps, that is, (W3, 1) by inference rules, write the process of the proof with the corresponding number of rules and facts (2-2) Method 2: Prove KB-w3,1 by contradiction to show KB ~ W31 is unsatifiable write the process of the proof with the correspondinExplanation / Answer
(2-1)
W1,3 => S1,2 V S1,4 V S2,3 -->(2)
The preceding equation says that a Wump exist in position 1,3 if and only if it could cause smell in its corresponding grids i.e in grids (1,2) or (1,4) or (2,3).
(2-1)
Now to prove that Wump is not there in position 3,1 by contradiction , let consider that Wump is there in position 3,1.
Let’s write the logic in predicate expression, and we know that Wump causes smell in corresponding squares.
So, W3,1 è S2,1 / S3,2 / S4,1 -->(2)
In Knowledge base axiom13 asserts that there is no smell in square S 2,1
~S2,1
Rewrite equation (2)
W3,1 è ~(~S2,1 ) / S3,2 / S4,1 -->(2)
W3,1 è ~(True) / S3,2 / S4,1
W3,1 è False / S3,2 / S4,1 --> (3)
Therefore W3,1 is False.
The contradiction is False thereby the initial assumption that Wump is not present in 3,1 is True.
So if we are able to prove the RHS in the equation (1) then it is evident that the position 1,3 contains a Wump.
Considering each of the predicates in the equation (1) .
Now looking at the axioms in the knowledge base,the axiom 16 , which is S1,2 exist and is true, SimilaryS1,4 and S2,3 is present in the knowledge base so all the RHS predicates exist in the knowledge base and it proves that Wump is present in position 1,3.
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