# predicate to clausal form

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hi, i'm studying Logic programming at the present and I came across this question on converting predicate to clausal form: All X All Y (uncle(x,y)) <-> Exists Z (parent(z,y) & brother (x,z)) Can someone explain the steps?

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The steps? You can't prove this identity without a definition for one of the predicates in terms of the others (presumably, uncle is defined in terms of parent and brother). Judging by the names, I can't think of a better definition for uncle than exactly what you posted.

Are you sure this is a question and not a definition? If so, you won't be able to verify it without some other identity relating parenthood, brotherhood and unclehood.

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we're not supposed to prove it. We have to convert it into clausal form :
Step 1 is given as removing the implication. Using P->Q = NOT P OR Q

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Well the first step is to convert it to prenex normal form, which is negation normal form (where you remove all implications etc and push negations in), but you also have to move the quantifiers to the front. You then skolemize which removes the existential quantifiers, and then you can drop your universal quanitifers as they're all at the front.

So the first step for you would be to convert the iff (<->) from A <-> to A -> B & B -> A. You then convert the implications as you stated.

Actually this may not be what you want to do, this is the proceedure when you're trying to prove a formula, you start by negating it and then performing the above proceedure to get it into clausal form. This proceedure will preserve consistancy, but not validity, so it's not really giving you the exact same thing at the end, prehaps a bit more detail on what you're trying to acomplish would be useful[/edit]

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