  We undertake a reconstruction of the epistemic significance of research on
operational theories in quantum foundations. We suggest that the space of
operational theories is analogous to the space of possible worlds employed in
the possible world semantics for modal logic, so research of this sort can be
understood as probing modal structure. Thus we argue that operational
axiomatisations of quantum mechanics may be interpreted as a novel form of
structural realism; we discuss the consequences of this interpretation for the
philosophy of structural realism and the future of operational theories.
