\begin{definition}[Definition:Consistent (Logic)/Proof System/Propositional Logic/Definition 1]
Let $\LL_0$ be the language of propositional logic.
Let $\mathscr P$ be a proof system for $\LL_0$.
Then $\mathscr P$ is '''consistent''' {{iff}}:
:There exists a logical formula $\phi$ such that $\not \vdash_{\mathscr P} \phi$
That is, some logical formula $\phi$ is '''not''' a theorem of $\mathscr P$.
Category:Definitions/Formal Systems
Category:Definitions/Propositional Logic
\end{definition}