Statements (17)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
gptkb:logic
gptkb:first-order_logic |
| gptkbp:contrapositive |
if a formula is not valid, then it is not provable
|
| gptkbp:guarantees |
no false theorems are provable
|
| https://www.w3.org/2000/01/rdf-schema#label |
Soundness theorem
|
| gptkbp:implies |
provability implies semantic truth
|
| gptkbp:opposedBy |
completeness theorem
|
| gptkbp:provenBy |
gptkb:David_Hilbert
gptkb:Kurt_Gödel |
| gptkbp:relatedTo |
completeness theorem
|
| gptkbp:state |
if a formula is provable, then it is valid
|
| gptkbp:usedIn |
gptkb:logic
model theory proof theory |
| gptkbp:bfsParent |
gptkb:Completeness_theorem
|
| gptkbp:bfsLayer |
5
|