2. (4 points) This is the Wumps world problem which has 4 x 4 squares PIT PIT PI
ID: 3605748 • Letter: 2
Question
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 Wii be true if there is a wumps in [ij] LetAJ, be true if there is a breeze in [i. J]. Let su 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 (1) (B1.1 (P1,2v P2,1)) (3) (B1.2(P1,1v P2.2 v P13)) (4) (B 1,3 (P1Zv P2,3 v P 14)) (5) (B3.1 (P2, 1wP32 v P4,l) (6) (S1.1 (W1Zv W2,1)) (7) (S 1,2 (W1, 1 v W2,2 v W1,2a) (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 that is, (W1,3) by inference rules. Write the (2-1) Method 1: Prove that position 1,3 has a process of the proof with the corresponding number of rules and facts (2-2) Method 2: Prove KB -W1,3 by contradiction to show KB A- W1,3 is unsatifiable Write the process of the proof with the corresponding number of rules and factsExplanation / Answer
Answer:-
(2-1) The preceding equation states 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).
W1,3 => S1,2 V S1,4 V S2,3 -->(1)
(2-2)Currently to prove that Wump is not there in position 3, 1 by contradiction, let study that Wump is there in position 3, 1. Let 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 statement 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 observing at the axioms in the knowledge base, the axiom 16 , which is S1,2 exist and is true, Likewise S1,4 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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