modal logic

2. Show that ◊A is a theorem of S.1 for nonmodal A iff A is a tautology. (Hint: use the unboxing lemma).

5. (i) Prove that if (A1∧... ∧An) ⊃An+1 is a nonmodal theorem then (□A1∧... ∧□An) ⊃□An+1 is a theorem. (You may use theorem 2.14.) (ii). Does this result hold with w in place of v? Justify your answer.

The proof of theorem 2.14 provides a derivation of □p⊃□q⊃□(p∧q) from □(p⊃q⊃(p∧q)).