In the context of a distributive lattice we specify the sort of mappings that could be generally called ''negations'' and study their behavior under iteration. We show that there are periodic and nonperiodic ones. Natural periodic negations exist with periods 2, 3, and 4 and pace 2, as well as natural nonperiodic ones, arising from the interaction of interior and quasi interior mappings with the pseudocomplement. For any n and any even $s<n$, negations of period n and pace s can also be constructed, but in a rather ad hoc and trivial way.
"Periodicity of Negation." Notre Dame J. Formal Logic 42 (2) 87 - 99, 2001. https://doi.org/10.1305/ndjfl/1054837935