Grammar 3 (cont.)

In Grammar 3, the first three Rules say a sentence (a string of type ), is either a rune (a string of type ), a foil (a string of type ), or formed by concatenating strings of those two types.

Rules 4 through 7 say a rune is either an empty string a blank symbol a paint or formed by concatenating strings of those three types.

Rule 8 characterizes a foil as a string of the form where is a tract.

The last two Rules say a tract is either a sentence or the concatenation of a tract, a comma, and a sentence, in that order.

At this point in the succession of grammars for the problematic applications of indefinite iterations, like the kleene star operator, are now reduced to finite forms of concatenation but the problems stemming from permitting non‑terminal symbols to cover both themselves and empty strings have yet to be resolved.

A moment’s reflection on the issue raises the general question:  What is a practical strategy for accounting for the empty string in the organization of any formal language which counts it among its sentences?

One answer presenting itself is the following:  If the empty string belongs to a formal language, it suffices to count it once at the beginning of the formal account which enumerates its sentences and then move on to more interesting materials.

Resources

• Cactus Language • Syntax
• Survey of Animated Logical Graphs
• Survey of Theme One Program

cc: Academia.edu • BlueSky • Laws of Form • Ma^thstodon • Research Gate
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science