For example, it is important to be able to discuss the validity of simulated model behavior with respect to the real system in a particular experimental frame. That is, validity is a relationship measured for a context. Another example of a meaningful relationship is whether a simulator such as a simulation program has been verified as representing the model adequately, again in the context specified by the experimental frame. Numerical approximations, for example, might be entirely acceptable in one frame, but a source of unacceptable error in another. As a result, theories require formalisms.
Formalisms are typically mathematical languages.
One example is the predicate calculus. Set theory is a common way to construct formalisms. The theory should specify means of composing models in the basic formalisms from more elementary pieces. One means of composing models is by connecting outputs to inputs. Such coupling should work on well-specified input and output interfaces, without reference to internal structure.