\begin{definition}[Definition:Inconsistent (Logic)]
Let $\LL$ be a logical language.
Let $\mathscr P$ be a proof system for $\LL$.
A collection $\FF$ of logical formulas is '''inconsistent for $\mathscr P$''' {{iff}}:
:For every logical formula $\phi$, $\FF \vdash_{\mathscr P} \phi$.
That is, ''every'' logical formula $\phi$ is a provable consequence of $\FF$.
{{expand}}
\end{definition}