Category:Complete Proof Systems
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This category contains results about Complete Proof Systems.
Definitions specific to this category can be found in Definitions/Complete Proof Systems.
Let $\LL$ be a logical language.
Let $\mathscr P$ be a proof system for $\LL$, and let $\mathscr M$ be a formal semantics for $\LL$.
Then $\mathscr P$ is said to be complete for $\mathscr M$ if and only if:
Symbolically, this can be expressed as the statement that, for every logical formula $\phi$ of $\LL$:
- $\models_{\mathscr M} \phi$ implies $\vdash_{\mathscr P} \phi$
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