Definition:Inconsistent (Logic)/Definition 1

Definition
Let $\LL$ be a logical language.

Let $\mathscr P$ be a proof system for $\LL$.

A set $\FF$ of logical formulas is inconsistent for $\mathscr P$ :


 * For every logical formula $\phi$, $\FF \vdash_{\mathscr P} \phi$.

That is, every logical formula $\phi$ is a provable consequence of $\FF$.

Also see

 * Equivalence of Definitions of Inconsistent (Logic)