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ZWMath›Logic›Proof theory›Logical completeness›ZW-LOGICAL-COMPLETENESS-005
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AreaLogicTopicProof theory
Propositional logic11
  • Proposition
  • Logical operator
  • Negation
  • Conjunction
  • Disjunction
  • Implication
  • Logical equivalence
  • NAND
  • Truth table
  • Tautology
  • Contradiction
Predicate logic5
  • Predicate
  • Universal quantifier
  • Existential quantifier
  • Negation of quantifiers
  • Order of quantifiers
Proof theory6
  • Axiomatic system
  • Rule of inference
  • Modus ponens
  • Formal proof
  • Consistency
  • Logical completeness
Completeness and incompleteness2
  • Gödel’s incompleteness
  • Arithmetic

Exercise · ZW-LOGICAL-COMPLETENESS-005 · ★☆☆ Basic

Completeness is mainly about what the calculus...

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  • A. Can prove

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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-004 Which expression represents the idea of completeness?
  • 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.

← ZW-LOGICAL-COMPLETENESS-004 ZW-LOGICAL-COMPLETENESS-006 →

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