A family of neighborhood contingency logics
This work solves specific theoretical problems in modal logic for researchers in formal logic, but it is incremental as it extends existing frameworks.
The paper addresses open questions in contingency logics by providing sound and complete axiomatizations for monotone and regular contingency logics using a canonical neighborhood function, building on prior work by Kuhn and Humberstone.
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.