  We analyze a class of modal logics rendered insensitive to reflexivity by way
of a modification to the semantic definition of the modal operator. We explore
the extent to which these logics can be characterized, and prove a general
completeness theorem on the basis of a translation between normal modal logics
and their reflexive-insensitive counterparts. Lastly, we provide a sufficient
semantic condition describing when a similarly general soundness result is also
available.
