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[Jun. 3rd, 2012|01:33 pm]
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Had some more interesting thoughts about that idea of embedding Pfenning-Davies modal logic into first-order focusing from a couple of days ago. I think I finally managed to split the PF diamond into two smaller connectives, and also found another couple of odd modalities that are easy to express in the image of the translation, and I don't have much intuition for them yet. And of course all of these (except for the lax-logic circle) depend on the Kripke accessibility relation, so you can get an even larger zoo of modalities by varying the axiomatization of that.