The logic of Bunched Implications (BI) provides a logical analysis of a basic notion of resource rich enough to provide ``pointer logic'' and ``separation logic'' semantics for programs which manipulate mutable data structures. In order to study the provability of such resource logics, we aim to emphasize the role of a semantic structure called resource graph from which we can generate proofs or countermodels. In this context, we provide a characterization of provability in BI's Pointer Logic (PL). Then, we present a new resource model, based on resource trees, and its related separation logic (BI-Loc), an extension of BI with a modality for locations, for which provability is studied.