Changes

A ''formal grammar'' <math>\mathfrak{G}</math> is given by a four-tuple <math>\mathfrak{G} = ( \, ^{\backprime\backprime} \, S \, ^{\prime\prime}, \, \mathfrak{Q}, \, \mathfrak{A}, \, \mathfrak{K} \, )</math> that takes the following form of description:

A ''formal grammar'' <math>\mathfrak{G}</math> is given by a four-tuple <math>\mathfrak{G} = ( \, ^{\backprime\backprime} \, S \, ^{\prime\prime}, \, \mathfrak{Q}, \, \mathfrak{A}, \, \mathfrak{K} \, )</math> that takes the following form of description:

<pre>

<ol style="list-style-type:decimal">

1.  "S" is the "initial", "special", "start", or "sentence symbol".

 

    Since the letter "S" serves this function only in a special setting,

<li><math>^{\backprime\backprime} S \, ^{\prime\prime}</math> is the ''initial'', ''special'', ''start'', or ''sentence'' symbol. Since the letter <math>^{\backprime\backprime} S \, ^{\prime\prime}</math> serves this function only in a special setting, its employment in this role need not create any confusion with its other typical uses as a string variable or as a sentence variable.</li>

    its employment in this role need not create any confusion with its

 

    other typical uses as a string variable or as a sentence variable.

2.  !Q! = {q_1, ..., q_m} is a finite set of "intermediate symbols",

<li><math>\mathfrak{A} = \{ a_1, \dots, a_n \}</math> is a finite set of ''terminal symbols'', also known as the ''alphabet'' of <math>\mathfrak{G},</math> all distinct from <math>^{\backprime\backprime} S \, ^{\prime\prime}</math> and disjoint from <math>\mathfrak{Q}.</math>  Depending on the particular conception of the language <math>\mathfrak{L}</math> that is ''covered'', ''generated'', ''governed'', or ''ruled'' by the grammar <math>\mathfrak{G},</math> that is, whether <math>\mathfrak{L}</math> is conceived to be a set of words, sentences, paragraphs, or more extended structures of discourse, it is usual to describe <math>\mathfrak{A}</math> as the ''alphabet'', ''lexicon'', ''vocabulary'', ''liturgy'', or ''phrase book'' of both the grammar <math>\mathfrak{G}</math> and the language <math>\mathfrak{L}</math> that it regulates.</li>

    all distinct from "S".

3.  !A! = {a_1, ..., a_n} is a finite set of "terminal symbols",

<li><math>\mathfrak{K}</math> is a finite set of ''characterizations''.  Depending on how they come into play, these are variously described as ''covering rules'', ''formations'', ''productions'', ''rewrite rules'', ''subsumptions'', ''transformations'', or ''typing rules''.</li>

    disjoint from !Q!.  Depending on the particular conception of the

    language !L! that is "covered", "generated", "governed", or "ruled"

    by the grammar !G!, that is, whether !L! is conceived to be a set of

    words, sentences, paragraphs, or more extended structures of discourse,

    that it regulates.

To describe the elements of !K! it helps to define some additional terms:

To describe the elements of !K! it helps to define some additional terms: