Logic/Inference by propositional logic

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* [[wikipedia:Propositional_calculus|Propositional calculus]]
* [[wikipedia:Propositional_calculus|Propositional calculus]]
* [[wikipedia:Modus_ponens|Modus ponens]]
* [[wikipedia:Modus_ponens|Modus ponens]]
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== Overview ==
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===Inference operator(⊢)===
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"α ⊢ β" means "assuming α, infer β.".
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* Double Negation elimination : "¬¬α ⊢ α"
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* Conjunction introduction : "α,β ⊢ α ∧β" , "α,β ⊢ β∧α"
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* Conjunction elimination : "α∧β ⊢ α" , "α∧β ⊢ β"
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* Disjunction introduction : α ⊢ α∨β , α ⊢ β∨α
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* Disjunction elimination : α∨β,¬β ⊢ α , α∨β,¬α ⊢ β
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* modus ponens : α,α→β ⊢ β
== CAI Exercise ==
== CAI Exercise ==
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[[en:Logic/Inference by propositional logic]]
[[en:Logic/Inference by propositional logic]]
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[[ja:論理学/命題論理]]
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[[ja:論理学/命題論理による推論]]

Latest revision as of 08:35, 23 May 2014

Logic > Inference by propositional logic

Contents

Contents

Overview

Inference operator(⊢)

"α ⊢ β" means "assuming α, infer β.".

  • Double Negation elimination : "¬¬α ⊢ α"
  • Conjunction introduction : "α,β ⊢ α ∧β" , "α,β ⊢ β∧α"
  • Conjunction elimination : "α∧β ⊢ α" , "α∧β ⊢ β"
  • Disjunction introduction : α ⊢ α∨β , α ⊢ β∨α
  • Disjunction elimination : α∨β,¬β ⊢ α , α∨β,¬α ⊢ β
  • modus ponens : α,α→β ⊢ β

CAI Exercise

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