Yarden Katz emailed me this query, which I unfortunately don’t have time right now to think about. Please, someone help him out by posting a comment!
I was reading Graham Priest’s account of intuitionist logic (in Intro to Non-Classical Logics), where he gives a possible world semantics for several intuitionist logics. In addition to few other restrictions in the semantics, the accessibility relation is essentially K + transitivity + symmetry. In parallel, I have been working on ground non-monotonic logics, especially on S5. K + trans + symmetry is obviously a subset of the universal structure used in S5, and this raised the following question for me: What would a non-monotonic intuitionist logic look like? Can it have a coherent philosophical interpretation? A bit of online searching brought nothing relevant, and I have not heard of such logics. I was wondering if you had any insights on this.