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

From Machinelearning
No edit summary
No edit summary
Line 6: Line 6:


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>
==References==
<references/>

Revision as of 05:27, 21 December 2018

Semantic completeness is sometimes written as: if Tϕ, then Tϕ.

Semantic completeness differs from negation completeness.

Definition

Smith's definition: a logic is semantically complete iff for any set of wffs Σ and any sentence ϕ, if Σϕ then Σϕ.[1]

References

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