Changes

To the extent that the issues of partialization become obvious at the level of symbols and can be dealt with by elementary syntactic means, they initially make their appearance in terms of the various ways that data can go missing.

To the extent that the issues of partialization become obvious at the level of symbols and can be dealt with by elementary syntactic means, they initially make their appearance in terms of the various ways that data can go missing.

The alternate notation <math>a \widehat{~} b\!</math> is provided for the ordered pair <math>(a, b).\!</math>  This choice of representation for ordered pairs is especially apt in the case of ''concrete indices'' and ''localized addresses'', where one wants the lead item to serve as a pointed reminder of the itemized content, as in <math>j \widehat{~} X_j = (j, X_j),\!</math> and it helps to stress the individuality of each member in the indexed family, as in the following set of equivalent notations.

The alternate notation "a^b" is provided for the ordered pair <a, b>. This choice of representation for ordered pairs is especially apt in the case of "concrete indices" (CIs) and "localized addresses" (LAs), where one wants the lead item to serve as a pointed reminder of the itemized content, as in i^Xi = <i, Xi>, and it helps to stress the individuality of each member in the indexed family, as in G = {Gj} = {j^Gj} = {<j, Gj>}.

 

| <math>G ~=~ \{ G_j \} ~=~ \{ j \widehat{~} G_j \} ~=~ \{ (j, G_j ) \}.\!</math>

|}

The "caret" (^) device works well in any situation where one desires to accentuate the fact that a formal subscript is being reclaimed and elevated to the status of an actual parameter.  By way of the operation indicated by the caret character the index bound to an object term can be rehabilitated as a full fledged component of an elementary relation, thereby schematically embedding the indicated object in the experiential space of a typical agent.

The ''binder'' device <math>(\,\widehat{~}~)\!</math> works well in any situation where one desires to accentuate the fact that a formal subscript is being reclaimed and elevated to the status of an actual parameter.  By way of the operation indicated by the caret character the index bound to an object term can be rehabilitated as a full-fledged component of an elementary relation, thereby schematically embedding the indicated object in the experiential space of a typical agent.

The form of the caret notation is intended to suggest the use of "pointers" and "views" in computational frameworks, letting one interpret "j^x" in any one of many various ways, for example:

The form of the caret notation is intended to suggest the use of "pointers" and "views" in computational frameworks, letting one interpret "j^x" in any one of many various ways, for example: