Right. is "the basic science of what simple rules do" not the same as Formal systems?
Formal Systems is the study of logical systems themselves.
Ruliology is a study of what actual systems do.
It's doing the arithmetic computations and looking at the results, not the abstract algebra.
In theory, theory and practice are the same. In practice, they are not.
A „logical” semantics can be assigned to such a formal system, but it is not a necessary entailment of the syntax, even if such systems are typically motivated by particular semantic models. Model theory might examine how the same formal system affords different interpretations.
Such syntactic systems have computational properties, and it is how computer science kicked off historically.
Assuming that you mean the same thing by "logical systems" and "actual systems", then Ruliology must fall under Formal Systems as a sub-discipline? Since studying "what these things do" is a subset of studying "these things themselves". And grounded on it.
If not, then what's the difference between "logical" and "actual" systems?