The Tableau Method (1) Normal Modal Logic

2023-2 Modal Logic (Segment 1)

① Determine whether the following valid in the systems indicated by the semantic tableau

1. L(Lp ⊃ Lq) ∨ L(Lq ⊃ Lp)
2. ML(p ⊃ LMp)

② Determine which of the following are valid in K, D, T, S4, S5, B by tableaux.

1. L(p ∨ Lq) .⊃. Lq ∨ Lp
2. M(p⊃p)
3. Mp ⊃ LMMp
4. Lp ∧ M(q ⊃ r) :⊃: L(p⊃q) ⊃ M(p ∧ r)