Definitions for

**"Formal system"**A set of rules for manipulating strings of symbols. Almost all notation in maths forms a formal system, they are the basic tools for doing maths.

a hierarchical grouping of sets of symbols or complete formulae, out of which other formulae can be generated, which can be accepted as valid

a rigidly defined kind of game that specifies rules for manipulating tokens

**Keywords:**grammar

a formal grammar

a system that allows us to prove things