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====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 requires in turn a number of auxiliary concepts and notations.  The notions of indication in question are expressed in a variety of different notations, enumerated as follows:

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 this array of conceptions and constructions.  Facilitating this task requires in turn a number of auxiliary concepts and notations.  The notions of indication in question are expressed in a variety of different notations, enumerated as follows:

# The functional language of propositions

# The functional language of propositions

# The geometric language of sets

# The geometric language of sets

Thus, one way to explain the relationships that exist among several concepts of indication is to describe the translations that must hold as a result between the associated families of notation.

Thus, one way to explain the relationships that exist among these concepts is to describe the ''translations'' that are induced among the allied families of notation.

===Syntactic Transformation Rules===

===Syntactic Transformation Rules===