User:IssaRice/Computability and logic/Semantic completeness

Semantic completeness is sometimes written as: if $T\models \varphi$, then $T⊢\varphi$.

Semantic completeness differs from negation completeness.

Definition

Smith's definition: a logic is semantically complete iff for any set of wffs $\mathrm{\Sigma }$ and any sentence $\varphi$, if $\mathrm{\Sigma }\models \varphi$ then $\mathrm{\Sigma }⊢\varphi$.