Suppose I'm asked to prove that one specific axiom from the list T, 4, B, D, 5 is not provable in some modal logic (KT, K4, KB, KD, K5, S4, S5, etc.). To be specific, suppose I'm asked to prove that 4 is not provable in K5 (I haven't checked if this is actually the case, but let's assume it's the case). How do I prove this by using soundness? Assuming the converse (that 4 is provable in K5), by soundness the axiom 4 is true at all points of all Euclidean models. Where to go from here?
2026-03-25 03:02:37.1774407757
About provability of modal axioms in modal logics
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Find a Euclidean model where an instance of 4 is false at some point in the model.