Assertion: order logic | /r/HasProperty | complete
Facets:
value: to distinguish it
type: PURPOSE
value: sometimes
type: TEMPORAL
value: under full semantics
type: OTHER
Source sentences:
text: In particular, the (semantic) logical consequence relation for second-order and higher-order logic is not semidecidable; there is no effective deduction system for second-order logic that is sound and complete under full semantics.
text: The second-order logic without these restrictions is sometimes called full second-order logic to distinguish it from the monadic version.
text: For example, Wagner (1987, 10–11) invokes Lindstrom’s theorem—that first-order logic is the only logic that is either complete or compact and satisfies the Löwenheim-Skolem theorem—in arguing that logic should be limited to first-order logic, and Kneale and Kneale (1962, 724, 741) invoke Gödel’s incompleteness theorems to similar effect.