Definition:Inconsistent (Logic)/Definition 2

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 $\mathscr P$ :


 * There exists a logical formula $\phi$ such that both
 * $\FF \vdash_{\mathscr P} \paren {\phi \land \neg \phi}$

Also see

 * Equivalence of Definitions of Inconsistent (Logic)