  We construct correspondences in logarithmic Hodge theory over a perfect field
of arbitrary characteristic. These are represented by classes in the cohomology
of sheaves of differential forms with log poles and, notably, log zeroes on
cartesian products of varieties. From one perspective this generalizes work of
Chatzistamatiou and R\"ulling, who developed (non-logarithmic) Hodge
correspondences over perfect fields of arbitrary characteristic; from another
we provide partial generalizations of more recent work of Binda, Park and
{\O}stv{\ae}r on logarithmic Hodge correspondences by relaxing finiteness and
strictness conditions on the correspondences considered.
