Looked up the definition of ‘simple interpretation’ in RDF model theory again. I thought I’d put a picture here for future reference. This is very similar to Pat’s Figure 1.
I’ve drawn V, IR, and IP as disjoint (except for the containment of LV in other things), but there is nothing in the definition that requires them to be. Of course IR and Pow(IR x IR) have to be disjoint due to the foundation axiom, but Pow(IR x IR) might overlap with IP.
The branching arrow is meant to indicate that IS maps V to IR union IP, that is to say, each member of V goes to either a member of IR or to a member of IP (or both, where IP and IP overlap). According to the definition LV has to include all the plain literals that are in V, and perhaps V and IR intersect in other ways (URIs might be resources).
There’s nothing in the definition that requires IS to map onto IR, i.e. the model theory spec doesn’t define a “resource” to be “something that is identified by a URI” and doesn’t even require every “property” to be a “resource”.