Logic/Inference by propositional logic
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Logic > Inference by propositional logic
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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