Question

HI, I NEED HELP ANSWERING PART C OF THIS QUESTION

There is a series of people standing in a line, from left to right. We’d like to reason about them using predicate logic. We have two predicates: End(x) which is true only if person x is standing at one of the two ends of the line, and LeftOf(x,y) which is true if person x is standing to the left of person y. We won’t use a RightOf(x,y) predicate, but rather just allow that LeftOf(y,x) means that x is to the right of y.

part a. Construct a knowledge base that represents the following axioms about the world. Each should take one predicate logic sentence.

i. LeftOf is a transitive operation.

ii. If a person is on the end, then everyone is on one side of him (either left or right).

iii. Exactly two people are at the end of the line.

iv. A person can’t be both to the left and to the right of the same person.

part b. Add statements to reflect the following observations about our line.

1. Alice is standing to the left of Bob.

2. Bob is standing to the left of Charles.

3. Diane is not standing to the left of Bob.

4. Diane is on one end of the line.

PART C Prove that Charles is standing to the left of Diane (i.e. show that is it entailed from the statements in parts a and b). Use proof by contradiction and resolution (on CNF formulae) (will be shown in class next time). Show your steps

Answer 1

It's given that, Diane is at one end of line i.e. Diane has either all others at its left or at its right.

Let ALICE=A,BOB=B,CHARLES=C,DIANE=D.

We know LeftOf(A, B) , LeftOf(B, C) and since D is not standing to the left of B, then its also true that D is on the right of A, B. Also Since D is at One End of the line, so D cant be at LeftOf C.

Hence we can say that the order of the line would be (A, B, C, D ).

So: Order of Line = ALICE, BOB, CHARLES, DIANE.

So proved, Charles is at the left of Diane.

Thanks and Regards.