 ##  [Formal System](/formal-system) 

  ##  [Formal System](https://mathlogic.quantumdictionary.io/formal-system-0) 

  
 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural &amp; Formal Sciences -

**Mathematics &amp; Logic Dictionary**

 
Definition

A precisely specified tuple consisting of a formal language (symbols and formation rules), a set of axioms or axiom schemas, and inference rules that determine how formulas may be derived; used to generate and manipulate formal expressions independent of any intended interpretation.