User:IssaRice/Computability and logic/Semantic completeness: Difference between revisions

Revision as of 05:26, 21 December 2018

Semantic completeness is sometimes written as: if $T\models \phi$ , then $T\vdash \phi$ .

Semantic completeness differs from negation completeness.

Definition

Smith's definition: a logic is semantically complete iff for any set of wffs $\Sigma$ and any sentence $\phi$ , if $\Sigma \models \phi$ then $\Sigma \vdash \phi$ .^[1]

↑ Peter Smith. An Introduction to Godel's Theorems. p. 33.

[1] Peter Smith. An Introduction to Godel's Theorems. p. 33.

[1]

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 Semantic completeness differs from [[../Negation completeness|negation completeness]].
+==Definition==
+Smith's definition: a ''logic'' is semantically complete iff for any set of wffs <math>\Sigma</math> and any sentence <math>\phi</math>, if <math>\Sigma \models \phi</math> then <math>\Sigma\vdash\phi</math>.<ref>Peter Smith. An Introduction to Godel's Theorems. p. 33.</ref>