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Revision as of 02:55, 30 August 2007
, 02:55, 30 August 2007→1.3.4.13. Formalization of OF : Objective Levels: markup
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 OG:
The standing relation of an OG is denoted by the symbol "<font face="system">:<s><</s></font>", pronounced ''set-in'', with either of the following two type-markings:
: <font face="system">:<s><</s></font> ⊆ ''J'' × ''P'' × ''Q'',
: <font face="system">:<s><</s></font> ⊆ ''J'' × ''X'' × ''X''.
The propping relation of an OG is denoted by the symbol "<font face="system">:<s>></s></font>", pronounced ''set-on'', with either of the following two type-markings:
: <font face="system">:<s>></s></font> ⊆ ''J'' × ''Q'' × ''P'',
: <font face="system">:<s>></s></font> ⊆ ''J'' × ''X'' × ''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''<sub>''j''</sub>}, 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''<sub>''j''</sub>}, then this generic interest is tantamount to having one's concern rest with the union of all the dyadic relations in the genre.
On these occasions, the assertion that (''x'', ''y'') ∈ <font size="+2">∪</font><sub>''J'' </sub>''G'' = ''G''<sub>''XX''</sub> can be indicated by any one of the following equivalent expressions:
On these occasions, the assertion that (''x'', ''y'') ∈ <font size="+2">∪</font><sub>''J'' </sub>''G'' = ''G''<sub>''XX''</sub> can be indicated by any one of the following equivalent expressions:
: G : x < y, x <G y, x < y : G,
:{| style="text-align:left; width:90%"
| ''G'' : ''x'' <font face="system">:<s><</s></font> ''y'' ,
| ''x'' <font face="system">:<s><</s></font><sub>''G''</sub> ''y'' ,
| ''x'' <font face="system">:<s><</s></font> ''y'' : ''G'' ,
|-
| ''G'' : ''y'' <font face="system">:<s>></s></font> ''x'' ,
| ''y'' <font face="system">:<s>></s></font><sub>''G''</sub> ''x'' ,
| ''y'' <font face="system">:<s>></s></font> ''x'' : ''G'' .
|}
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 j and two objects x and y belongs to the standing relation of the OG, ‹j, x, y› ? :<, or equally, to indicate that a triple consisting of an OM j and two objects y and x belongs to the propping relation of the OG, ‹j, y, x› ? :>, all of the following notations are equivalent:
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 j and two objects x and y belongs to the standing relation of the OG, ‹j, x, y› ? :<, or equally, to indicate that a triple consisting of an OM j and two objects y and x belongs to the propping relation of the OG, ‹j, y, x› ? :>, all of the following notations are equivalent: