Not quite. A formal system is a system of syntactic rules defined over an alphabet of symbols. They can be mechanized in principle. Peano arithmetic is one example.

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.