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Minimal logic

Minimal logic, or minimal calculus, is a symbolic logic system originally developed by Ingebrigt Johansson under the name "Minimalkalkül". It is a paraconsistent logic weaker than intuitionistic logic that rejects the principle of explosion (ex falso quodlibet), according to which any statement can be proven from a contradiction, as well as the law of…

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Overview

Syntax and axiomatization

Theorems

Relation to classical logic

Relation to intuitionistic logic

Relation to type theory

Semantics

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Minimal logic

Nodes56
Edges55
Triples102
Avg. degree1.96
Density0.035714
Components1

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Minimal logic

Top relations

related to References · 62
Minimal logic → Afstudeerscriptie, Almudena, Anne Sjerp, Archived, Basic Proof Theory, Calculi, Cambridge University Press, Case Studies, Christine, Colacito, Compositio Mathematica, Computation, Computer Science, Curry-Howard Isomorphism, Deduction, Der Minimalkalkül, Deva, Discrete Design, Formal Structures, Formalismus
related to Relation to intuitionistic logic · 6
Minimal logic → Any, As, Both, But, In, The
related to Axiomatization via absurdity · 5
Minimal logic → Any, Constructively, If, One, To
related to Relation to classical logic · 5
Minimal logic → Considering, In, Indeed, The, Therefore
related to Simple types · 5
Minimal logic → Delta, Functional, Gamma, In, The
related to Relation to relevance logic · 4
Minimal logic → Minimal, That, The, With
related to Syntax and axiomatization · 4
Minimal logic → Alternative, Minimal, Such, Using
related to Axiomatization via alternative principles · 3
Minimal logic → All, Instead, This
related to Relation to paraconsistent logic · 3
Minimal logic → Excluded, In, Minimal
is a · 2
Minimal logic → implication, same as the positive

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Important terminology

displaystyle logic neg minimal negation also lor explosion land intuitionistic bot big principle implication equivalent double case introduction form may

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Minimal logicis aimplication0.90text
Minimal logicis asame as the positive0.90text
Minimal logicrelated to Axiomatization via absurdityOne0.60section
Minimal logicrelated to Axiomatization via absurdityTo0.60section
Minimal logicrelated to Axiomatization via absurdityConstructively0.60section
Minimal logicrelated to Axiomatization via absurdityAny0.60section
Minimal logicrelated to Axiomatization via absurdityIf0.60section
Minimal logicrelated to Axiomatization via alternative principlesAll0.60section
Minimal logicrelated to Axiomatization via alternative principlesInstead0.60section
Minimal logicrelated to Axiomatization via alternative principlesThis0.60section
Minimal logicrelated to Negation introductionOver0.60section
Minimal logicrelated to ReferencesLock-green0.60section

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