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A short note I wrote a few months ago just got published: https://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/2293-06.pdf
I show that diamonds are already embedded in Artemov and Protopopescu's intuitionistic epistemic logic (they are just double negations).
This is part of some work I'm doing to understand diamonds in intuitionistic modal logics.