It depends on how the phrase "humanities logic" is used.
If you're referring to formal techniques that are applied to the
language used in the study of religion, philosophy, history,
etcetera, then "humanities logic" refers to propositional logic,
predicate logic, and set theory. In this way, the use of logic is
analogous to the way that the social and behavioral sciences use
statistics, and to the way that the natural sciences use math and
statistics.
Should you be referring to logic outside of a math department
setting, then you're referring to logic as it is taught in most
philosophy departments.
When you're referring to logic that is not symbol based, then
you may be talking about informal logic