There is a curious sort of diagnostic clue which often serves to reveal the dominance of one mode or the other within an individual thinker’s cognitive style.  Examined on the question of what constitutes the natural numbers, an additive thinker tends to start the sequence at 0 while a multiplicative thinker tends to regard it as beginning at 1.

In any style of description, grammar, or theory of a language, it is usually possible to tease out the influence of the contrasting traits, namely, the additive attitude versus the multiplicative tendency which go to make up the style in question, and even to determine the dominant inclination or point of view which establishes its perspective on the target domain.

In each style of formal grammar, the multiplicative aspect is present in the sequential concatenation of signs, in both the augmented strings and the terminal strings.  In settings where the non‑terminal symbols classify types of strings, the concatenation of the non-terminal symbols signifies the cartesian product over the corresponding sets of strings.

In the context‑free style of formal grammar, the additive aspect is easy to spot.  It is signaled by the parallel covering of many augmented strings or sentential forms by the same non‑terminal symbol.  In active terms, it calls for the independent rewriting of that non‑terminal symbol by a number of different successors, as in the following scheme.

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