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Revision as of 00:05, 30 August 2007
, 00:05, 30 August 2007→1.3.4.13. Formalization of OF : Objective Levels: markup
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.
: UJG = Uj Gj = {‹x, y› ? X?X : ‹x, y› ? Gj for some j ? J}.
:<p><math>\textstyle \bigcup_J G = \textstyle \bigcup_j G_j = \{ (x, y) \in X \times X : (x, y) \in G_j\ \mbox{for some}\ j \in J \} .</math></p>
When the relevant genre is contemplated as a triadic relation, G ? J?X?X, then one is dealing with the projection of G on the object dyad XxX.
When the relevant genre is contemplated as a triadic relation, ''G'' ⊆ ''J'' × ''X'' × ''X'', then one is dealing with the projection of ''G'' on the object dyad ''X'' × ''X''.
: GXX = ProjXX(G) = {‹x, y› ? X?X : ‹j, x, y› ? G for some j ? J}.
: GXX = ProjXX(G) = {‹x, y› ? X?X : ‹j, x, y› ? G for some j ? J}.