sequent calculus
E846921
Sequent calculus is a formal logical system introduced by Gerhard Gentzen that represents deductions as sequences (sequents) to analyze and structure proofs, especially in proof theory and logic.
Statements (57)
| Predicate | Object |
|---|---|
| instanceOf |
deductive system
ⓘ
formal system ⓘ logical calculus ⓘ proof calculus ⓘ |
| appliesTo |
classical logic
ⓘ
intuitionistic logic ⓘ modal logic ⓘ substructural logics ⓘ |
| basedOn | sequents ⓘ |
| centralResult | cut elimination theorem NERFINISHED ⓘ |
| enables |
normalization of proofs
ⓘ
subformula property ⓘ |
| field |
mathematical logic
ⓘ
philosophical logic ⓘ proof theory ⓘ |
| hasComponent |
antecedent
ⓘ
succedent ⓘ |
| hasFeature |
explicit structural rules
ⓘ
fine-grained control of inference steps ⓘ symmetry between left and right rules ⓘ |
| hasLogicalRule |
elimination rule
ⓘ
introduction rule ⓘ |
| hasProperty | cut elimination theorem ⓘ |
| hasRuleType |
initial sequent
ⓘ
logical rule ⓘ structural rule ⓘ |
| hasStructuralRule |
contraction
ⓘ
cut ⓘ exchange ⓘ weakening ⓘ |
| hasVariant |
LJ
NERFINISHED
ⓘ
LK NERFINISHED ⓘ classical sequent calculus ⓘ intuitionistic sequent calculus ⓘ multiple-conclusion sequent calculus ⓘ single-conclusion sequent calculus ⓘ |
| influenced |
linear logic
ⓘ
separation logic NERFINISHED ⓘ structural proof theory ⓘ type theory ⓘ |
| introducedBy | Gerhard Gentzen NERFINISHED ⓘ |
| purpose |
analyze structure of proofs
ⓘ
establish consistency proofs ⓘ formalize logical deduction ⓘ study proof transformations ⓘ |
| relatedTo |
Hilbert-style systems
ⓘ
natural deduction ⓘ |
| represents | deductions as sequents ⓘ |
| typicalSequentForm | Γ ⊢ Δ GENERATED ⓘ |
| usedFor |
automated theorem proving
ⓘ
completeness proofs ⓘ consistency proofs ⓘ interpolation theorems ⓘ proof search ⓘ |
| usesNotation | Γ ⊢ Δ ⓘ |
| yearIntroduced |
1934
ⓘ
1935 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.