Refining the notions of operational theories, ontological models, and noncontextuality

We revise the traditional notion of an operational theory in a manner which separates out the procedural, epistemic, propositional, causal, and inferential aspects of an operational theory. In an analogous way we refine the traditional notion of an ontological theory. Given these, we can define an ontological model via a structure-preserving map from an operational theory to an ontological theory. Consequently, we also refine the traditional concepts of operational equivalence and Spekkens’ notion of generalised contextuality. In doing all this, we resolve a slew of formal problems, ambiguities and conceptual confusions surrounding the traditional notions. Moreover, our new definitions apply to arbitrary operational scenarios allowing us to consider situations well beyond the simple prepare-measure case.