Exercise · ZW-LOGICAL-COMPLETENESS-004 · ★☆☆ Basic
Which expression represents the idea of completeness?
Choose one option.
Show answer
- A. If it is valid, then it is provable
Review the concept: Logical completeness
A calculus \(\mathcal{S}\) is complete if every formula \(\varphi\) that is valid under its semantics is provable in \(\mathcal{S}\).
\[\mathcal{S}\models\varphi\Rightarrow\mathcal{S}\vdash\varphi\]
More practice problems: logical completeness
- ZW-LOGICAL-COMPLETENESS-001 Completeness relates...
- ZW-LOGICAL-COMPLETENESS-002 In a complete calculus, a valid formula can...
- ZW-LOGICAL-COMPLETENESS-003 Completeness does not mean that...
- ZW-LOGICAL-COMPLETENESS-005 Completeness is mainly about what the calculus...
- ZW-LOGICAL-COMPLETENESS-006 The completeness of a calculus connects...
- ZW-LOGICAL-COMPLETENESS-007 If a valid formula is provable in the calculus, we speak of...
- ZW-LOGICAL-COMPLETENESS-008 Completeness should not be read as saying that...
- ZW-LOGICAL-COMPLETENESS-009 Select consequences of a complete calculus.