0
$\begingroup$

Say we have a formula in CNF like so:

$$ \{ A , A \} \{\neg A \}$$

where A can be any formula you could think of.

Abviously this formula can never be true (since $ A \land \neg A$ can never be true) , and should "resolve" to the empty clause. But if I "naively" apply the first resolution step I would get $\{A\}$ as a resolvent of the above clauses, which of course is not the empty clause.

Can someone tell me what is the correct resolvent of the above formula or how I should resolve this formula correctly ?

$\endgroup$
1
$\begingroup$

You should never have duplicates in your clauses, so $\{ A, A \}$ immediately becomes $\{ A \}$. This is why they are treated as sets, so as to make sure duplicates never occur!

As another example: suppose you resolve $\{ A, B \}$ with $\{ \neg A, B \}$. Then the result is $\{ B \}$, rather than $\{ B,B \}$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.