This article proposes the axiomatizations of contingency logics of various natural classes of neighborhood frames. In particular, by defining a suitable canonical neighborhood function, we give sound and complete axiomatizations of monotone contingency logic and regular contingency logic, thereby answering two open questions raised by Bakhtiari, van Ditmarsch, and Hansen. The canonical function is inspired by a function proposed by Kuhn in 1995. We show that Kuhn’s function is actually equal to a related function originally given by Humberstone.
Jie Fan. "A Family of Neighborhood Contingency Logics." Notre Dame J. Formal Logic 60 (4) 683 - 699, November 2019. https://doi.org/10.1215/00294527-2019-0025