# Syntax

[https://en.wikipedia.org/wiki/Syntax\_(logic](https://en.wikipedia.org/wiki/Syntax_\(logic))

Syntax is concerned with the rules (grammar) governing the manipulation of expressions that constitute the _well-formed formulas_ (wff) of a formal system and its formal language.

A well-formed formula (wff) is a syntactically valid string in a formal language, as opposed to the myriad of other, nonsense, strings.

Syntactic entities of formal languages:

* symbol
* formula
* system
* theorem
* proof
* interpretation

Symbols and strings may be divided into nonsense and well-formed formulas. _A formal language is identical to the set of its well-formed formulas_. The wff set may be divided into _theorems_ and _non-theorems_.

> theorems ⊂ non-theorems ⊂ wff ⊂ all lang strings

symbols -> strings ↓ ↙ formulas --> atoms (atomic formulas) --> complex formulas ├─ nonsense formulas └─ well-formed formulas ├─ non-theorems └─ theorems
