Cactus Language • Preliminaries 15

A notation of the form S :> T was introduced last time to indicate a category of grammatical relationships whose sense is suggested by any of the following readings.

\begin{array}{l}  S ~\mathrm{covers}~ T  \\[2pt]  S ~\mathrm{governs}~ T  \\[2pt]  S ~\mathrm{rules}~ T  \\[2pt]  S ~\mathrm{subsumes}~ T  \\[2pt]  S ~\mathrm{types~over}~ T  \end{array}

For the moment it’s enough to call S :> T a covering relation, reading it as S ~\mathrm{covers}~ T.

In what follows the letter ``S" indicates the type of a sentence in the contemplated language \mathfrak{L}.  The letter ``S" is the initial symbol or sentence symbol of the candidate formal grammar for \mathfrak{L}.

Generally speaking, any number of letters like ``T", signifying other types of strings, will be found necessary for a reasonable account or rational reconstruction of the sentences in \mathfrak{L}.  The additional letters are known as intermediate symbols and collected together in the set \mathfrak{Q}.

Combining the singleton set \{ ``S" \} whose sole member is the initial symbol with the set \mathfrak{Q} of intermediate symbols results in the set \{ ``S" \} \cup \mathfrak{Q} of non‑terminal symbols.  Even though \mathfrak{Q} is strictly only the set of intermediate symbols, it is handy to use q as a typical variable ranging over the full set of non‑terminal symbols, q \in \{ ``S" \} \cup \mathfrak{Q}.

To complete the package, the alphabet \mathfrak{A} of the language \mathfrak{L} may also be referred to as the set of terminal symbols.

Resources

cc: Academia.edu • BlueSky • Laws of FormMathstodonResearch Gate
cc: Conceptual GraphsCyberneticsStructural ModelingSystems Science

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