User:IssaRice/Computability and logic/Semantic completeness: Difference between revisions
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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> | 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> | ||
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Revision as of 05:27, 21 December 2018
Semantic completeness is sometimes written as: if , then .
Semantic completeness differs from negation completeness.
Definition
Smith's definition: a logic is semantically complete iff for any set of wffs and any sentence , if then .[1]
References
- ↑ Peter Smith. An Introduction to Godel's Theorems. p. 33.