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" | ||
| + | * 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 == | == CAI Exercise == | ||
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[[en:Logic/Inference by propositional logic]] | [[en:Logic/Inference by propositional logic]] | ||
| - | [[ja:論理学/ | + | [[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
