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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 binder symbol 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 ''link'' 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 link symbol 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 binder notation is intended to suggest the use of ''pointers'' and ''views'' in computational frameworks, letting one interpret <math>j \widehat{~} x\!</math> in several different ways, for example, any one of the following.

The form of the link notation is intended to suggest the use of ''pointers'' and ''views'' in computational frameworks, letting one interpret <math>j \widehat{~} x\!</math> in several different ways, for example, any one of the following.

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<p align="center">'''Fragments'''</p>

<p align="center">'''Fragments'''</p>

I would like to record here, in what is topically the appropriate place, notice of a number of open questions that will have to be addressed if anyone desires to make a consistent calculus out of this binder notation.  Perhaps it is only because the franker forms of liaison involved in the couple <math>a \widehat{~} b\!</math> are more subject to the vagaries of syntactic elision than the corresponding bindings of the anglish ligature <math>(a, b),\!</math> but for some reason or other the circumflex character of these diacritical notices are much more liable to suggest various forms of elaboration, including higher order generalizations and information-theoretic partializations of the very idea of <math>n\!</math>-tuples and sequences.

I would like to record here, in what is topically the appropriate place, notice of a number of open questions that will have to be addressed if anyone desires to make a consistent calculus out of this link notation.  Perhaps it is only because the franker forms of liaison involved in the couple <math>a \widehat{~} b\!</math> are more subject to the vagaries of syntactic elision than the corresponding bindings of the anglish ligature <math>(a, b),\!</math> but for some reason or other the circumflex character of these diacritical notices are much more liable to suggest various forms of elaboration, including higher order generalizations and information-theoretic partializations of the very idea of <math>n\!</math>-tuples and sequences.

One way to deal with the problems of partial information &hellip;

One way to deal with the problems of partial information &hellip;