What is the definition of grammar?

Answer 1

1. a particular analysis of the system and structure of language or of a specific language.

2. the whole system and structure of a language or of languages in general, usually taken as consisting of syntax and morphology (including inflections) and sometimes also phonology and semantics.

A mathematical definition for grammar :

A grammar G is a 4 tuple (VN , Ʃ, P, S) where :

1. VN is a finite non-empty set of variables. [like , ... ]
2. Ʃis a finite non-empty set of terminal strings.

[This is like substituting the noun or verb with a word. noun = 'wiki'. verb = 'running' . So the words 'wiki', 'running' etc are terminal strings. i.e. they are constants. ]

1. P is the set of production rules.

[Production rules are those instructions which when applied to a sentence of the form ... would give you a sentence in the language (here it is in English) ] Production rules are of the form α → β , where α, β ϵ ( VN Ս Ʃ)*

1. S is the special symbol denoting the sentence.

e.g in English it would be like , S = ...

A language L(G) is generated by applying the production rules on S to generate a string of terminals alone (called a sentence).

e.g. :VN = { noun, verb, adverb }

Ʃ = { 'wiki', 'running', 'swiftly', 'away' }

S =

P = { noun -> 'wiki' , verb -> 'running' , -> 'quickly' }

So from S on applying the production rules we generate a string of terminals : wiki swiftly running

This forms our final result. Since we have obtained a sentence with only terminals.

In most grammars ( for machines or humans ) there could be recursive production rules that could form innumerable number of terminal sentences. And it would be quite a task to verify if a given sentence belongs to the language.
Answer

Grammar is the correct wording of words, to form sentences.
grammar |ˈgramər|nounthe whole system and structure of a language or of languages in general, usually taken as consisting of syntax and morphology (including inflections) and sometimes also phonology andsemantics.


Grammar may also be defined as: Grammar is the science of the study of the behavior of words and the rules governing the use of words in sentences.