2023-2 Modal Logic (Segment 2)
Q) Quantification theory may be formalized this way:
Prove the following in the systems indicated.
1. ├ L(∀x)ϕx . ⊃. (∀x)Lϕx
2. ├ β (∀x)Lϕx . ⊃. L(∀x)ϕx (Recall that system β is T + p ⊃ LMp. )
3. ├ M(∃x)ϕx . ⊃. (∃x)Mϕx (The system is QML + (∀x)Lϕx . ⊃. L(∀x)ϕx)
4. ├ (∀x)Lα ⊃ L(∀x)α (The system is QML+ (∀x)L(α ⊃ β) .⊃. L((∀x)α ⊃ (∀x)β)
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