Operationalism eschews a notion of system state in favour of the empirical behaviours of preparation and measurement. Abramsky has formalized operational structures as Chu spaces. It would be nice to know that there is a mathematical prescription, involving the Chu spaces (or some other model of operational structure), that generates an ontic state space. This could be used to form a foundation for physics. In this model, we build a notion of an ontic state space based on our interaction with a laboratory system. I guess this is in contrast to normal physics and science, where we posit the form of an ontic state space and then prove where it works and does not work. Has anyone seen work that attempts to take operationalist structures and develop an ontic state space?