I was wondering if someone can perhaps help with this proving. I am not sure how to handle a temporal frame that is not a set of only natural numbers. Any suggestions?
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You handle this exactly the same way you would if the frame would consist of natural numbers. What have you tried? You should also be open about this being a homework question, if it is one. Is it one?
If you want to disprove it, find a valuation and a rational number q where your sentence is not true. Otherwise you show that it is true independent of the valuation.
Let's assume we want to prove it. We choose a rational number q, and assume the left side: q⊨◻◻p. Is it true that q⊨◻p? If so, then for any from q accessible world r, i.e. for any r>q we have to show that r⊨p. Can you take it from here? (Hint: The following is the wrong approach: By assumption, q⊨◻◻p. Therefore r⊨◻p. Now you are stuck.)