Changes

====1.3.12.  Syntactic Transformations====

====1.3.12.  Syntactic Transformations====

We have been examining several distinct but closely related notions of indication.  To discuss the import of these ideas in greater depth, it serves to establish a number of logical relations and set-theoretic identities that can be found to hold among their roughly parallel arrays of conceptions and constructions.  Facilitating this task, in turn, requires a number of auxiliary concepts and notations.

We have been examining several distinct but closely related notions of indication.  To discuss the import of these ideas in greater depth, it serves to establish a number of logical relations and set-theoretic identities that can be found to hold among their roughly parallel arrays of conceptions and constructions.  Facilitating this task requires in turn a number of auxiliary concepts and notations.

The diverse notions of indication presently under discussion are expressed in a variety of different notations, enumerated as follows:

The diverse notions of indication presently under discussion are expressed in a variety of different notations, enumerated as follows:

# The geometric language of sets

# The geometric language of sets

Correspondingly, one way to explain the relationships that exist among the various notions of indication is to describe the translations that they induce among the associated families of notation.

Correspondingly, one way to explain the relationships that exist among the various notions of indication is to describe the translations that they

induce among the associated families of notation.

=====1.3.12.1.  Syntactic Transformation Rules=====

=====1.3.12.1.  Syntactic Transformation Rules=====

A good way to summarize the necessary translations between different styles of indication, and along the way to organize their use in practice, is by means of the "rules of syntactic transformation" (ROSTs) that partially formalize the translations in question.

A good way to summarize the necessary translations between different styles of indication, and along the way to organize their use in practice, is by means of the ''rules of syntactic transformation'' (ROSTs) that partially formalize the translations in question.

Rudimentary examples of ROSTs are readily mined from the raw materials that are already available in this area of discussion.  To begin as near the beginning as possible, let the definition of an indicator function be recorded in the following form:

Rudimentary examples of ROSTs are readily mined from the raw materials that are already available in this area of discussion.  To begin as near the beginning as possible, let the definition of an indicator function be recorded in the following form: