In logic, a logical system is said to be formal when it uses a specific set of rules to manipulate symbols without regard to their meaning or interpretation.

In a formal logical system, the meaning of the symbols used is not important; what is important is the formal structure of the system and the rules that govern the manipulation of symbols. This allows the system to be used to reason about any subject matter, as long as it can be expressed using the symbols of the system.

The meaning of sentences expressed by the symbols of a formal system of logic is gleaned when one or more automatons apply and/or share an interpretation of the formal system.

Formal logical systems are typically used to study mathematical, philosophical, and linguistic concepts. They can be used to prove logical and mathematical theorems, study the properties of formal languages, and analyze arguments in natural language.

A formal logical system typically consists of a set of axioms, a set of rules of inference, and a set of symbols that can be used to represent logical formulas. The axioms are basic logical statements that are taken as true without proof, and the rules of inference specify how new formulas can be derived from existing ones. The symbols are used to represent logical connectives (such as "and", "or", and "not"), quantifiers (such as "for all" and "there exists"), and variables (which can take on different values).