A sequence of neighborhood contingency logics

TL;DR

This paper develops axiomatizations for contingency logic using neighborhood semantics, providing solutions to open questions and linking canonical functions to historical functions by Kuhn and Humberstone.

Contribution

It introduces new axiomatizations for monotone and regular contingency logic with neighborhood semantics, resolving previously open problems.

Findings

Established sound and complete axiomatizations for monotone contingency logic.

Linked Kuhn's canonical function to Humberstone's function.

Answered open questions in the field of contingency logic.

Abstract

This note proposes various axiomatizations of contingency logic under neighborhood semantics. 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.