Non-monotonic intuitionist logic?

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.

3 thoughts on “Non-monotonic intuitionist logic?”

1. Anonymous says:

I’m not quite sure what’s meant by “non-monotonic” in this context, but my paper “Subintuitionistic Logics” considers modifications of the usual Kripke semantics for intuitionistic logic to live without the transitivity of information inclusion, its reflexivity, or the preservation of formulas up the “inclusion” relation.The paper is available as a preprint on my site  and on the NDJFL site here.The work has been taken up in another paper by Celani and Jansana, also in the NDJFL, here.  Posted by Greg Restall

2. Anonymous says:

Thanks to Prof. Zach for posting my question. I had a typo; I meant “reflexivity” not “symmetry” in my original post.Thanks for the pointer to the NDJFL paper, I will read it. As for non-monotonicity: I’m not sure how to be specific. The logic I am comparing it to (non-mon ground S5) is one that has negation as failure semantics and closed world assumption. Monotonicity is therefore not preserved. Thanks, –Yarden Posted by Yarden Katz

3. Anonymous says:

Google Scholar  turned up this:D.M. Gabbay, Intuitionistic basis for non-monotonic logic, Proceedings of the 6th Conference on Automated Deduction, LNCS, Vol.138, Springer-Verlag, Berlin, 1982, pp. 260-273.H Wansing. Semantics-based Nonmonotonic Inference. Notre Dame Journal of Formal Logic, 1995Fischer Servi, Gisèle. Nonmonotonic consequence based on intuitionistic logic. J. Symb. Log. 57, No.4, 1176-1197 (1992).Amati G.; Carlucci-Aiello L; Pirri F. Intuitionistic Autoepistemic Logic. Studia Logica, July 1997, vol. 59, no. 1, pp. 103-120(18)  Posted by Richard Zach