Gentzen-style proof systems
E846923
Gentzen-style proof systems are formal logical calculi, such as natural deduction and sequent calculi, that rigorously structure proofs using inference rules to clarify the foundations of mathematics and logic.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
deductive system
ⓘ
formal system ⓘ logical calculus ⓘ proof system ⓘ |
| aimsAt |
analysis of proof structure
ⓘ
clarification of logical consequence ⓘ completeness with respect to semantics ⓘ rigorous formalization of proofs ⓘ |
| appliesTo |
classical logic
ⓘ
intuitionistic logic NERFINISHED ⓘ modal logics ⓘ substructural logics ⓘ |
| basedOn |
derivation trees
ⓘ
sequents ⓘ |
| characterizedBy |
rule-based derivations
ⓘ
stepwise application of rules ⓘ syntactic notion of proof ⓘ |
| contrastedWith | Hilbert-style proof systems NERFINISHED ⓘ |
| developedInContextOf | foundational studies of arithmetic ⓘ |
| ensures | soundness with respect to semantics ⓘ |
| field |
foundations of mathematics
ⓘ
mathematical logic ⓘ proof theory ⓘ |
| hasAdvantageOver | Hilbert-style systems in proof analysis ⓘ |
| hasComponent |
elimination rules
ⓘ
introduction rules ⓘ logical rules ⓘ structural rules ⓘ |
| hasForm |
natural deduction
ⓘ
sequent calculus ⓘ |
| influenced |
lambda calculus-based proof systems
ⓘ
modern type theory ⓘ structural proof theory ⓘ |
| namedAfter | Gerhard Gentzen NERFINISHED ⓘ |
| relatedTo |
analytic proofs
ⓘ
cut rule ⓘ proof search ⓘ subformula property ⓘ |
| supports |
cut-elimination theorems
ⓘ
normalization theorems ⓘ structural analysis of inference ⓘ |
| usedFor |
analysis of proof complexity
ⓘ
automated theorem proving ⓘ consistency proofs ⓘ proof normalization ⓘ |
| usedIn |
formal verification
ⓘ
logic programming ⓘ |
| uses | inference rules ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.