Assertion: logic | /r/HasProperty | complete
Facets:
value: weakly
type: DEGREE
value: without compactness
type: OTHER
value: with respect to this semantics
type: OTHER
value: in superintuitionistic and modal logics
type: OTHER
value: structurally
type: DEGREE
Source sentences:
text: In superintuitionistic and modal logics, a logic is structurally complete if every admissible rule is derivable.
text: Kant famously claimed, in Logic (1800), that logic was the one completed science, and that Aristotelian logic more or less included everything about logic there was to know.
text: that is, the logic axiomatized by (A1)–(A7) — is sound and complete with respect to this semantics (Leblanc and Thomason 1968).
text: Without compactness, a logic might be weakly complete (every valid formula is provable in the axiomatic system), but not strongly complete (for every set \(\Gamma\) of formulas, every logical consequence of \(\Gamma\) is provable from \(\Gamma\) in the axiomatic system).