There are few proposals to improve the interactivity and control of wave function collapse (WFC) in a mixed-initiative setting. Moreover, most WFC algorithm variants operate on an simple, unstructured set of tiles. This limitation on the level of control provided to designers hampers their creative work in various ways. We propose Hierarchical Semantic WFC, a generalized approach to WFC that organizes its tile-set into a hierarchy akin to a taxonomy induced by the relation 'consists-of'. In such a hierarchical structure, abstract tiles (i.e. non-leaf nodes) can represent the first sketchy intentions of a designer (e.g. forest, urban, desert,...) This allows a designer to interactively collapse a given area into abstract tiles, while subsequently, (and repeatedly, if desired) WFC can resolve each area into a variety of particular instances, by further collapsing it into (a valid combination of) its children tiles (whether leaves or not). We identify how this subtle tile-set change affects the whole WFC algorithm, describe a number of novel exploratory and interactive functions that this enables, and showcase these with a variety of examples generated with our prototype implementation. We conclude that these new mixed-initiative content generation methods can considerably reduce design iteration times and improve the assistance given to designers in expressing their creative intent.