0
$\begingroup$

For two proposition logical formulas $\phi$ and $\chi$ so that $\phi\implies\chi$ is generally valid. How can I prove that there is a formular $\psi$ with $var(\psi )\subseteq var(\phi )\cap var(\chi )$ so that $\phi\implies\psi$ and $\psi\implies\chi$ are generally valid?

$\endgroup$
2
$\begingroup$

The formula $\psi$ is called an interpolant and the method of finding such an interpolant is called Craig interpolation. On the Wikipedia article you can find more information about it, including a proof that interpolants always exist in propositional logic.

$\endgroup$

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.