This paper proposes a new approach to open argument functions in LFG. As opposed to both the earliest approach, under which open argument functions were individuated by category (VCOMP, NCOMO, PCOMP, ACOMP), and the conventional approach, under which there is a single category-neutral open argument function (XCOMP), this paper proposes that there are three open argument functions, XOBJ-theta, XOBL-theta, and XCOMP, each of which is canonically associated with one or more c-structure categories, much like their closed counterparts.