Syntax (logic)

The symbols, formulas, systems, theorems and proofs expressed in formal languages are syntactic entities whose properties may be studied without regard to any meaning they may be given, and, in fact, need not be given any.

In computer science, the term syntax refers to the rules governing the composition of well-formed expressions in a programming language.

For instance there are logical constants which do not refer to any idea, but rather serve as a form of punctuation in the language (e.g. parentheses).

A formal language is a syntactic entity which consists of a set of finite strings of symbols which are its words (usually called its well-formed formulas).

Formation rules are a precise description of which strings of symbols are the well-formed formulas of a formal language.

It is synonymous with the set of strings over the alphabet of the formal language which constitute well formed formulas.

[2] A proposition is identified ontologically as an idea, concept or abstraction whose token instances are patterns of symbols, marks, sounds, or strings of words.

Gödel's incompleteness theorem shows that no recursive system that is sufficiently powerful, such as the Peano axioms, can be both consistent and complete.

This diagram shows the syntactic entities which may be constructed from formal languages . [ 1 ] The symbols and strings of symbols may be broadly divided into nonsense and well-formed formulas . A formal language is identical to the set of its well-formed formulas. The set of well-formed formulas may be broadly divided into theorems and non-theorems.