Changes

It is important to emphasize that the index set <math>J\!</math> and the particular attachments of indices to dyadic relations are part and parcel to <math>G\!</math>, befitting the concrete character intended for the concept of an objective genre, which is expected to realistically embody in the character of each <math>G_j\!</math> both ''a local habitation and a name''.  For this reason, among others, the <math>G_j\!</math> can safely be referred to as ''individual dyadic relations''.  Since the classical notion of an ''individual'' as a ''perfectly determinate entity'' has no application in finite information contexts, it is safe to recycle this term to distinguish the ''terminally informative particulars'' that a concrete index <math>j\!</math> adds to its thematic object <math>G_j\!</math>.

It is important to emphasize that the index set <math>J\!</math> and the particular attachments of indices to dyadic relations are part and parcel to <math>G\!</math>, befitting the concrete character intended for the concept of an objective genre, which is expected to realistically embody in the character of each <math>G_j\!</math> both ''a local habitation and a name''.  For this reason, among others, the <math>G_j\!</math> can safely be referred to as ''individual dyadic relations''.  Since the classical notion of an ''individual'' as a ''perfectly determinate entity'' has no application in finite information contexts, it is safe to recycle this term to distinguish the ''terminally informative particulars'' that a concrete index <math>j\!</math> adds to its thematic object <math>G_j\!</math>.

Depending on the prevailing direction of interest in the genre ''G'', <math>\lessdot</math> or <math>\gtrdot</math>, the same symbol is used equivocally for all the relations <math>G_j\!</math>.  The <math>G_j\!</math> can be regarded as formalizing the objective motives that make up the genre <math>G\!</math>, provided it is understood that the information corresponding to the parameter <math>j\!</math> constitutes an integral part of the ''motive'' or ''motif'' of <math>G_j\!</math>.

Depending on the prevailing direction of interest in the genre <math>G\!</math>, <math>\lessdot</math> or <math>\gtrdot</math>, the same symbol is used equivocally for all the relations <math>G_j\!</math>.  The <math>G_j\!</math> can be regarded as formalizing the objective motives that make up the genre <math>G\!</math>, provided it is understood that the information corresponding to the parameter <math>j\!</math> constitutes an integral part of the ''motive'' or ''motif'' of <math>G_j\!</math>.

In this formulation, <math>G\!</math> constitutes ''ontological hierarchy'' of a plenary type, one that determines the complete array of objects and relationships that are conceivable and describable within a given discussion.  Operating with reference to the global field of possibilities presented by <math>G\!</math>, each <math>G_j\!</math> corresponds to the specialized competence of a particular agent, selecting out the objects and links of the generic hierarchy that are known to, owing to, or owned by a given interpreter.

In this formulation, <math>G\!</math> constitutes ''ontological hierarchy'' of a plenary type, one that determines the complete array of objects and relationships that are conceivable and describable within a given discussion.  Operating with reference to the global field of possibilities presented by <math>G\!</math>, each <math>G_j\!</math> corresponds to the specialized competence of a particular agent, selecting out the objects and links of the generic hierarchy that are known to, owing to, or owned by a given interpreter.

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On these occasions, the assertion that (''x'',&nbsp;''y'') &isin; <font size="+2">&cup;</font>_''J''&nbsp;''G'' = ''G''_''XX'' can be indicated by any one of the following equivalent expressions:

On these occasions, the assertion that <math>(x, y)\!</math> is in <math>\cup_J G = G_{XX}</math> can be indicated by any one of the following equivalent expressions:

:{| style="text-align:left; width:90%"

{| align="center" cellpadding="8" style="text-align:center; width:75%"

| ''G'' : ''x'' <math>\lessdot</math> ''y''&nbsp;,

| <math>G : x \lessdot y,</math>

| ''x'' <math>\lessdot</math>_''G'' ''y''&nbsp;,

| <math>x \lessdot_G y,</math>

| ''x'' <math>\lessdot</math> ''y'' : ''G''&nbsp;,

| <math>x \lessdot y : G,</math>

|-

|-

| ''G'' : ''y'' <math>\gtrdot</math> ''x''&nbsp;,

| <math>G : y \gtrdot x,</math>

| ''y'' <math>\gtrdot</math>_''G'' ''x''&nbsp;,

| <math>y \gtrdot_G x,</math>

| ''y'' <math>\gtrdot</math> ''x'' : ''G''&nbsp;.

| <math>y \gtrdot x : G.</math>

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At other times explicit mention needs to be made of the ''interpretive perspective'' or ''individual dyadic relation'' (IDR) that links two objects.  To indicate that a triple consisting of an OM&nbsp;''j'' and two objects ''x'' and ''y'' belongs to the standing relation of the OG, in symbols, (''j'',&nbsp;''x'',&nbsp;''y'')&nbsp;&isin;&nbsp;<math>:\!\lessdot</math>, or equally, to indicate that a triple consisting of an OM&nbsp;''j'' and two objects ''y'' and ''x'' belongs to the propping relation of the OG, in symbols, (''j'',&nbsp;''y'',&nbsp;''x'')&nbsp;&isin;&nbsp;<math>:\!\gtrdot</math>, all of the following notations are equivalent:

At other times explicit mention needs to be made of the ''interpretive perspective'' or ''individual dyadic relation'' that links two objects.  To indicate that a triple consisting of a motive <math>j\!</math> and two objects <math>x\!</math> and <math>y\!</math> belongs to the standing relation of the genre, in symbols, <math>(j, x, y) \in\ :\!\lessdot</math>, or equally, to indicate that a triple consisting of a motive <math>j\!</math> and two objects <math>y\!</math> and <math>x\!</math> belongs to the propping relation of the genre, in symbols, <math>(j, y, x) \in\ :\!\gtrdot</math>, all of the following notations are equivalent:

:{| style="text-align:left; width:90%"

{| align="center" cellpadding="8" style="text-align:center; width:75%"

| ''j'' : ''x'' <math>\lessdot</math> ''y''&nbsp;,

| <math>j : x \lessdot y,</math>

| ''x'' <math>\lessdot</math>_''j'' ''y''&nbsp;,

| <math>x \lessdot_j y,</math>

| ''x'' <math>\lessdot</math> ''y'' : ''j''&nbsp;,

| <math>x \lessdot y : j,</math>

|-

|-

| ''j'' : ''y'' <math>\gtrdot</math> ''x''&nbsp;,

| <math>j : y \gtrdot x,</math>

| ''y'' <math>\gtrdot</math>_''j'' ''x''&nbsp;,

| <math>y \gtrdot_j x,</math>

| ''y'' <math>\gtrdot</math> ''x'' : ''j''&nbsp;.

| <math>y \gtrdot x : j.</math>

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