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# The ''multiplicative'' or ''serial'' styles favor ''products of sums'' <math>(\textstyle\prod\sum)</math> as canonical forms of expression, pulling products, intersections, concatenations, and logical conjunctions to the outermost layers of analysis and synthesis, while pushing sums, unions, co-products, and logical disjunctions to the innermost levels of articulation and generation.  In propositional logic, this style leads to the ''conjunctive normal form'' (CNF).

# The ''multiplicative'' or ''serial'' styles favor ''products of sums'' <math>(\textstyle\prod\sum)</math> as canonical forms of expression, pulling products, intersections, concatenations, and logical conjunctions to the outermost layers of analysis and synthesis, while pushing sums, unions, co-products, and logical disjunctions to the innermost levels of articulation and generation.  In propositional logic, this style leads to the ''conjunctive normal form'' (CNF).

There is a curious sort of diagnostic clue that 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.

There is a curious sort of diagnostic clue, a veritable shibboleth,

that 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

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

usually possible to tease out the influence of these contrasting traits,

namely, the "additive" attitude versus the "mutiplicative" tendency that

go to make up the particular style in question, and even to determine the

dominant inclination or point of view that establishes its perspective on

the target domain.

In each style of formal grammar, the "multiplicative" aspect is present

In each style of formal grammar, the ''multiplicative'' aspect is present in the sequential concatenation of signs, both in the augmented strings and in 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 sequential concatenation of signs, both in the augmented strings

and in 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

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

easy enough to spot.  It is signaled by the parallel covering of many

augmented strings or sentential forms by the same non-terminal symbol.

Expressed in active terms, this calls for the independent rewriting

of that non-terminal symbol by a number of different successors,

as in the following scheme:

| q    :>    W_1.

| q    :>    W_1.

|

|