Logic and the set theory - Lecture 9: Predicate Calculus

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Inference rules for the universal quantifiersExamplesFa A. ⊢ ∀xAx. This is incorrect.∀x(Fx → Gx), Fa → Ga, : Fa : Ga, : ∀xGx, Fa → ∀xGx. This isincorrect.∀xLxx A., Laa, ∀zLza. This is incorrect.∀x(Fx ∧ Gx) ⊢ ∀xFx ∧ ∀xGx.Proof: 1. ∀x(Gx ∧ Fx) A.2. Fa ∧ Ga from 1.3. Fa.4. Gb.5. ∀xFx.6. ∀xGx.S. Choi (KAIST) Logic and set theory October 7, 2012 8 / 26
Inference rules for the universal quantifiersExamplesFa A. ⊢ ∀xAx. This is incorrect.∀x(Fx → Gx), Fa → Ga, : Fa : Ga, : ∀xGx, Fa → ∀xGx. This isincorrect.∀xLxx A., Laa, ∀zLza. This is incorrect.∀x(Fx ∧ Gx) ⊢ ∀xFx ∧ ∀xGx.Proof: 1. ∀x(Gx ∧ Fx) A.2. Fa ∧ Ga from 1.3. Fa.4. Gb.5. ∀xFx.6. ∀xGx.7. ∀xFx ∧ ∀xGx.S. Choi (KAIST) Logic and set theory October 7, 2012 8 / 26
Page 2 and 3: IntroductionAbout this lectureReaso
Page 10 and 11: IntroductionSome helpful references
Page 18 and 19: Inference rules for the universal q
Page 66 and 67: Inference rules for existential qua
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Inference rules for existential qua
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Logic and the set theory - Lecture 9: Predicate Calculus

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