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Dialectica interpretation

In proof theory, the Dialectica interpretation is a proof interpretation of intuitionistic logic (Heyting arithmetic) into a finite type extension of primitive recursive arithmetic, the so-called System T. It was developed by Kurt Gödel to provide a consistency proof of arithmetic. The name of the interpretation comes from the journal Dialectica, where…

Linear logic, Overview & Motivation

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Overview

Motivation

Intuitionistic logic

Linear logic

Variants

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Dialectica interpretation

Nodes32
Edges31
Triples23
Avg. degree1.94
Density0.0625
Components1

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Dialectica interpretation

Top relations

related to Linear logic · 7
Dialectica interpretation → Although, Dialectica, Girard's, Paiva's, Shirahata's, Since, The Dialectica
related to Variants · 7
Dialectica interpretation → Comprehensive, Dialectica, Diller-Nahm, Ferreira-Oliva, Kohlenbach's, Kőnig's, Several
related to Motivation · 6
Dialectica interpretation → Gentzen, Gödel, Gödel's, Heyting, Peano, Via
related to Extensions · 2
Dialectica interpretation → Intuitively, The
is a · 1
Dialectica interpretation → proof interpretation of intuitionistic logic

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Important terminology

interpretation dialectica arithmetic proof heyting system intuitionistic logic displaystyle translation consistency gödel's formula classical linear given formulas gödel induction via

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Dialectica interpretationis aproof interpretation of intuitionistic logic0.90text
Dialectica interpretationrelated to ExtensionsThe0.60section
Dialectica interpretationrelated to ExtensionsIntuitively0.60section
Dialectica interpretationrelated to Linear logicThe Dialectica0.60section
Dialectica interpretationrelated to Linear logicGirard's0.60section
Dialectica interpretationrelated to Linear logicDialectica0.60section
Dialectica interpretationrelated to Linear logicSince0.60section
Dialectica interpretationrelated to Linear logicAlthough0.60section
Dialectica interpretationrelated to Linear logicShirahata's0.60section
Dialectica interpretationrelated to Linear logicPaiva's0.60section
Dialectica interpretationrelated to MotivationVia0.60section
Dialectica interpretationrelated to MotivationGödel0.60section

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