Logarithmic de Rham--Witt complexes via the D\'ecalage operator

We provide a new formalism of de Rham–Witt complexes in the logarithmic setting. This construction generalizes a result of Bhatt–Lurie–Mathew, and agrees with those of Hyodo–Kato and Matsuue for log-smooth schemes of log-Cartier type. We then apply our formalism to obtain a more direct proof of the log crystalline comparison of A_inf-cohomology in the case of semistable reduction, which is established by Cesnavicius–Koshiwara.