We consider the modal logic of non-contingency in a general setting, without making special assumptions about the accessibility relation. The basic logic in this setting is axiomatized, and some of its extensions are discussed, with special attention to the expressive weakness of the language whose sole modal primitive is non-contingency (or equivalently, contingency), by comparison with the usual language based on necessity (or equivalently, possibility).
"The Logic of Non-contingency." Notre Dame J. Formal Logic 36 (2) 214 - 229, Spring 1995. https://doi.org/10.1305/ndjfl/1040248455