A moment’s reflection on the issue of style, giving due consideration to the received array of stylistic choices, ought to inspire at least the question:  “Are those the only choices there are?”

There are abundant indications that other options, more differentiated varieties of description and more integrated ways of approaching individual languages, are likely to be conceivable, feasible, and even more ultimately viable.  If a suitably generic style, one that incorporates the full scope of logical combinations and operations, is broadly available, then it would no longer be necessary, or even apt, to argue in universal terms about which style is best, but more useful to investigate how we might adapt the local styles to the local requirements.  The medium of a fully generic style would yield a viable compromise between additive and multiplicative canons and render the choice between parallel and serial a false alternative, at least, when expressed in the globally exclusive terms which are currently and most commonly adopted to pose it.

One set of indications comes from the study of machines, languages, and computation, including theories of their structures and relations.  The forms of composition and decomposition known as parallel and serial are merely the limiting special cases in two directions of specialization of a more generic form, commonly known as the cascade form of combination.  That is a well‑known fact in the theories dealing with automata and their associated formal languages but its implications do not seem to be widely appreciated outside those fields.  In particular, the availability of that option dispells the need to choose one extreme or the other, since most of the natural cases are likely to exist somewhere in between.

Another set of indications appears in algebra and category theory, where forms of composition and decomposition related to the cascade combination, namely, the semi‑direct product and its special case, the wreath product, are encountered at higher levels of generality than the cartesian products of sets or the direct products of spaces.

In those domains of operation, one finds it necessary to consider also the co‑product of sets and spaces, a construction which artificially creates a disjoint union of sets, that is, a union of spaces which are being treated as independent.  It does that, in effect, by indexing, coloring, or preparing the otherwise possibly overlapping domains which are being combined.  What renders that a chimera or a hybrid form of combination is the fact that the indexing is tantamount to a cartesian product of a singleton set, namely, the conventional index, color, or affix in question, with the individual domain which is entering as a factor, a term, or a participant in the final result.

Resources

• Cactus Language • Pragmatics
• 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