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==Syntactic Transformations==
To discuss the import of the above definitions 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.
To discuss the import of the above definitions 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 diverse notions of ''indication'' under discussion are expressed in a variety of different notations, in particular, the logical language of sentences, the functional language of propositions, and the geometric language of sets. Thus, one way to explain the relationships that exist among these concepts is to describe the ''translations'' that they induce among the allied families of notation.
The diverse notions of ''indication'' under discussion are expressed in a variety of different notations, in particular, the logical language of sentences, the functional language of propositions, and the geometric language of sets. Thus, one way to explain the relationships that exist among these concepts is to describe the ''translations'' that they induce among the allied families of notation.
===Syntactic Transformation Rules===
A good way to summarize these translations and to organize their use in practice is by means of the ''syntactic transformation rules'' (STRs) that partially formalize them. A rudimentary example of a STR is readily mined from the raw materials that are already available in this area of discussion. To begin, let the definition of an indicator function be recorded in the following form:
A good way to summarize these translations and to organize their use in practice is by means of the ''syntactic transformation rules'' (STRs) that partially formalize them. A rudimentary example of a STR is readily mined from the raw materials that are already available in this area of discussion. To begin, let the definition of an indicator function be recorded in the following form:
