Category:Sound Proof Systems

This category contains results about Sound Proof Systems.
Definitions specific to this category can be found in Definitions/Sound Proof Systems.

Let $\LL$ be a logical language.

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

Let $\mathscr M$ be a formal semantics for $\LL$.

Then $\mathscr P$ is said to be sound for $\mathscr M$ if and only if:

Every $\mathscr P$-theorem is an $\mathscr M$-tautology.

Symbolically, this can be expressed as the statement that, for every logical formula $\phi$ of $\LL$:

$\vdash_{\mathscr P} \phi$ implies $\models_{\mathscr M} \phi$