Changes

There is a ''partial converse'' of the standing relation that transposes the order in which the two object domains are mentioned.  This is called the ''propping relation'' of the OG, and it can be taken as an alternate way of defining the genre.

There is a ''partial converse'' of the standing relation that transposes the order in which the two object domains are mentioned.  This is called the ''propping relation'' of the OG, and it can be taken as an alternate way of defining the genre.

:<p><math>G\!\uparrow \ = \ \{(j, q, p) \in J \times Q \times P : (j, p, q) \in G \} ,</math></p>

| <math>G\!\uparrow \ = \ \{(j, q, p) \in J \times Q \times P : (j, p, q) \in G \},</math>

: or

or:

:<p><math>G\!\uparrow \ = \ \{(j, y, x) \in J \times X \times X : (j, x, y) \in G \} .</math></p>

| <math>G\!\uparrow \ = \ \{(j, y, x) \in J \times X \times X : (j, x, y) \in G \}.</math>

The following conventions are useful for discussing the set-theoretic extensions of the staging relations and staging operations of an OG:

The following conventions are useful for discussing the set-theoretic extensions of the staging relations and staging operations of an objective genre:

The standing relation of an OG is denoted by the symbol "<math>:\!\lessdot</math>", pronounced ''set-in'', with either of the following two type-markings:

The standing relation of a genre is denoted by the symbol <math>:\!\lessdot</math>, pronounced ''set-in'', with either of the following two type-markings:

: <math>:\!\lessdot</math>&nbsp;&sube;&nbsp;''J''&nbsp;&times;&nbsp;''P''&nbsp;&times;&nbsp;''Q'',

| <math>:\!\lessdot\ \subseteq\ J \times P \times Q,</math>

| <math>:\!\lessdot\ \subseteq\ J \times X \times X.</math>

: <math>:\!\lessdot</math>&nbsp;&sube;&nbsp;''J''&nbsp;&times;&nbsp;''X''&nbsp;&times;&nbsp;''X''.

The propping relation of an OG is denoted by the symbol <math>:\!\gtrdot</math>, pronounced ''set-on'', with either of the following two type-markings:

The propping relation of an OG is denoted by the symbol "<math>:\!\gtrdot</math>", pronounced ''set-on'', with either of the following two type-markings:

{| align="center" cellpadding="8"

 

| <math>:\!\gtrdot\ \subseteq\ J \times Q \times P,</math>

: <math>:\!\gtrdot</math>&nbsp;&sube;&nbsp;''J''&nbsp;&times;&nbsp;''Q''&nbsp;&times;&nbsp;''P'',

 

| <math>:\!\gtrdot\ \subseteq\ J \times X \times X.</math>

: <math>:\!\gtrdot</math>&nbsp;&sube;&nbsp;''J''&nbsp;&times;&nbsp;''X''&nbsp;&times;&nbsp;''X''.

Often one's level of interest in a genre is ''purely generic''.  When the relevant genre is regarded as an indexed family of dyadic relations, ''G'' = {''G''_''j''}, then this generic interest is tantamount to having one's concern rest with the union of all the dyadic relations in the genre.

Often one's level of interest in a genre is ''purely generic''.  When the relevant genre is regarded as an indexed family of dyadic relations, ''G'' = {''G''_''j''}, then this generic interest is tantamount to having one's concern rest with the union of all the dyadic relations in the genre.