User:Marshallsumter/Dominant group/Rigorous definition

What is a rigorous definition of "dominant group"?

Notation
Notation: let the symbol Def. indicate that a definition is following.

Universals
To help with definitions, their meanings and intents, there is the learning resource theory of definition.

Axiomatic definition
The rigorous definition fulfills the axioms that define a metadefinition so that a generalized definition can be defined using an appropriate function that fulfills the axioms. Having met these axioms as a criteria of a general definition, the definition is said to be a rigorous definition.

An axiomatic definition is a rigorous definition: "the definition must clearly state the rules that are considered as binding, and on the other hand give the implementor enough freedom to achieve efficiency by leaving certain less important aspects undefined."

Genera differentia
The term "dominant group" appears to be used to identify entities of importance. The genera differentia for possible relative synonyms of "dominant group" fall into the following set of orderable pairs:

'Orderable' means that any synonym from within the first category can be ordered with any synonym from the second category to form an alternate term for "dominant group"; for example, "superior class", "influential sect", "master assembly", "most important group", and "dominant painting". "Dominant" falls into category 171. "Group" is in category 61. Further, any word which has its most or much more common usage within these categories may also form an alternate term, such as "ruling group", where "ruling" has its most common usage in category 739, or "dominant party", where "party" is in category 74. "Taxon" or "taxa" are like "species" in category 61. "Society" is in category 786 so there is a "dominant society".

When one or two orderable pairs are produced, the results are
 * 1) one pair - relative synonym,
 * 2) one pair in which the first or second category has each of two from a category - definition, and
 * 3) two pairs from two to four categories - definition.

Meaningless dominant group
Each subject area within which the term "dominant group" is used has the same problem: "unless and until a rigorous definition of the term 'dominant group' is rendered, the argument fails to establish its conclusion due to the fact that one of its premises is meaningless."

Rigorous definition
Def. a category synonym for "group", including "group", and a category synonym for "dominant", including "dominant", that as one or two orderable pairs has only the properties of two pairs: i.e., from two to four categories [exclusive], or one pair in which the first or second category has up to each of two from a category is called a rigorous definition of dominant group.

Temporal encoding
"[A] rigorous definition for the term temporal encoding" "relies on the identification of an encoding time window".

Def. "the duration of a neuron's spike train assumed to correspond to a single symbol in the neural code" is called "an encoding time window".

Theorem: "[t]he duration of the encoding time window is dictated by the time scale of the information being encoded."