Perhaps I ought to comment on the differences between the present and the standard definition of a formal grammar, since I am attempting to strike a compromise with several alternative conventions of usage, and thus to leave certain options open for future exploration.  All the changes are minor, in the sense they are not intended to alter the classes of languages able to be generated but only to clear up the ambiguities and obscurities affecting their conception.

Perhaps most importantly, the conventional scope of non‑terminal symbols is expanded to include the sentence symbol, mainly on account of all the contexts where initial and intermediate symbols are naturally invoked in the same breath.  By way of compensating for the usual exclusion of the sentence symbol from the non‑terminal class an equivalent distinction is introduced in the fashion of a distinction between the initial and the intermediate symbols, and that serves its purpose in all the contexts where the two kinds of symbols need to be treated separately.

At present I remain a bit worried about the motivations and the justifications for introducing that distinction in the first place.  It is purportedly designed to guarantee that the process of derivation at least gets started in a definite direction, while the real question has to do with how it all ends.  The excuses of efficiency and expediency I offered as reasons for distinguishing between empty and significant sentences are likely to be ephemeral, if not entirely illusory, since intermediate symbols are still permitted to characterize or cover themselves, not to mention being allowed to cover the empty string, and so the very types of traps one exerts oneself to avoid at the outset are always there to afflict the process at all the intervening times.

If one reflects on the form of grammar being prescribed here, it looks as if one sought, rather futilely, to avoid the problems of recursion by proscribing the main program from calling itself, while allowing any subprogram to do so.  But any trouble avoidable in the part is also avoidable in the main, while any trouble inescapable in the part is also inescapable in the main.  Consequently, I am reserving the right to change my mind at a later stage, perhaps to permit the initial symbol to characterize, cover, produce, or regenerate itself, if that turns out to be the best way in the end.

Resources

• Cactus Language • Stylistics
• 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