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, 03:39, 3 January 2009→The Cactus Language : Syntax: markup
# To express the fact or to make the assertion that each member of a specified set of strings <math>T \subseteq \mathfrak{A}^*</math> also belongs to the syntactic category <math>S,\!</math> the one that qualifies a string as being a sentence in the relevant formal language <math>\mathfrak{L}.</math>
# To express the fact or to make the assertion that each member of a specified set of strings <math>T \subseteq \mathfrak{A}^*</math> also belongs to the syntactic category <math>S,\!</math> the one that qualifies a string as being a sentence in the relevant formal language <math>\mathfrak{L}.</math>
# To specify the intension or to signify the intention that every string that fits the conditions of the abstract type <math>T\!</math> must also fall under the grammatical heading of a sentence, as indicated by the type <math>S,\!</math> all within the target language <math>\mathfrak{L}.</math>
# To specify the intension or to signify the intention that every string that fits the conditions of the abstract type <math>T\!</math> must also fall under the grammatical heading of a sentence, as indicated by the type <math>S,\!</math> all within the target language <math>\mathfrak{L}.</math>
In these types of situation the letter <math>S,\!</math> that signifies the type of a sentence in the language of interest, is called the ''initial symbol'' or the ''sentence symbol'' of a candidate formal grammar for the language, while any number of letters like <math>T,\!</math> signifying other types of strings that are necessary to a reasonable account or a rational reconstruction of the sentences that belong to the language, are collectively referred to as ''intermediate symbols''.
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Combining the singleton set {"S"} whose sole member is the initial symbol
Combining the singleton set {"S"} whose sole member is the initial symbol
with the set !Q! that assembles together all of the intermediate symbols
with the set !Q! that assembles together all of the intermediate symbols