You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
8 lines
599 B
8 lines
599 B
\item
|
|
The soundness of natural deduction for propositional logic can be proven via a \emph{mathematical course-of-values induction on the length of the Natural Deduction proof}. Let $M(k)$ be the following assertion:
|
|
|
|
$M(k)\coloneqq$ „For all sequents $\phi_1,\phi_2,\dots,\phi_n\vdash \psi$ which have a proof of length $k$,
|
|
it is the case that $\phi_1,\phi_2,\dots,\phi_n\models \psi$ holds.”
|
|
|
|
Discuss the \textbf{induction step}
|
|
$M(1)\wedge M(2) \wedge \dots \wedge M(k-1) \rightarrow M(k)$ under the assumption that the \textbf{$\andi$} was applied as a final rule to prove the conclusion.
|