A criterion for log regularity via log Frobenius-Witt differentials

T. Saito introduced FW-derivations and the modules of FW-differentials. He gave a regularity criterion in terms of the modules of FW-differentials. In this paper, we introduce logarithmic analogues of FW-derivations and the modules of FW-differentials. We study basic properties of them and give a logarithmic regularity criterion in terms of the modules of logarithmic FW-differentials.