Directory:Jon Awbrey/Papers/Syntactic Transformations - Revision history

Jon Awbrey: '''Author: Jon Awbrey'''

2015-12-09T22:14:10Z

'''Author: Jon Awbrey'''

Jon Awbrey: test edit

2015-12-07T23:10:04Z

test edit

Jon Awbrey: /* 1.3.12. Syntactic Transformations */ "their roughly parallel arrays of conceptions and constructions"

2010-09-03T01:48:14Z

1.3.12. Syntactic Transformations: "their roughly parallel arrays of conceptions and constructions"

Jon Awbrey: + section numbers

2010-09-03T01:22:48Z

+ section numbers

Jon Awbrey: /* 1.3.12. Syntactic Transformations */

2010-09-03T01:14:56Z

1.3.12. Syntactic Transformations

Jon Awbrey: /* 1.3.12. Syntactic Transformations */ trim

2010-09-03T01:14:17Z

1.3.12. Syntactic Transformations: trim

Jon Awbrey: /* Syntactic Transformations */ integrate other version

2010-09-03T01:06:33Z

Syntactic Transformations: integrate other version

Jon Awbrey: /* Syntactic Transformation Rules */ figits

2009-02-20T19:14:28Z

Syntactic Transformation Rules: figits

Jon Awbrey: /* Syntactic Transformation Rules */ fix typos

2009-02-20T18:34:40Z

Syntactic Transformation Rules: fix typos

Jon Awbrey: /* Syntactic Transformation Rules */ editing note + cleanup

2009-02-20T17:48:32Z

Syntactic Transformation Rules: editing note + cleanup

← Older revision		Revision as of 22:14, 9 December 2015
Line 1:		Line 1:
	{{DISPLAYTITLE:Syntactic Transformations}}		{{DISPLAYTITLE:Syntactic Transformations}}
		+	'''Author: [[User:Jon Awbrey\|Jon Awbrey]]'''

	<div class="nonumtoc">__TOC__</div>		<div class="nonumtoc">__TOC__</div>

← Older revision		Revision as of 23:10, 7 December 2015
Line 2,976:		Line 2,976:
	\| Excerpt: Subsections 1.3.10.8 - 1.3.10.13		\| Excerpt: Subsections 1.3.10.8 - 1.3.10.13
	</pre>		</pre>
		+
		+	***

@@ Line 5: / Line 5: @@
 ====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 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:
+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:
 # The functional language of propositions

@@ Line 11: / Line 11: @@
 # The geometric language of sets
-Thus, one way to explain the relationships that hold among these concepts is to describe the ''translations'' that are induced among the allied families of notation.
+Thus, one way to explain the relationships that hold among these concepts is to describe the ''translations'' that are induced among their allied families of notation.
-===Syntactic Transformation Rules===
+=====1.3.12.1.  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:
@@ Line 1,518: / Line 1,518: @@
 <br>
-===Derived Equivalence Relations===
+=====1.3.12.2.  Derived Equivalence Relations=====
 One seeks a method of general application for approaching the individual sign relation, a way to select an aspect of its form, to analyze it with regard to its intrinsic structure, and to classify it in comparison with other sign relations.  With respect to a particular sign relation, one approach that presents itself is to examine the relation between signs and interpretants that is given directly by its connotative component and to compare it with the various forms of derived, indirect, mediate, or peripheral relationships that can be found to exist among signs and interpretants by way of secondary considerations or subsequent studies.  Of especial interest are the relationships among signs and interpretants that can be obtained by working through the collections of objects that they commonly or severally denote.
@@ Line 2,439: / Line 2,439: @@
 <br>
-===Digression on Derived Relations===
+=====1.3.12.3.  Digression on Derived Relations=====
 A better understanding of derived equivalence relations (DERs) can be achieved by placing their constructions within a more general context and thus comparing the associated type of derivation operation, namely, the one that takes a triadic relation <math>L\!</math> into a dyadic relation <math>\operatorname{Der}(L),</math> with other types of operations on triadic relations.  The proper setting would permit a comparative study of all their constructions from a basic set of projections and a full array of compositions on dyadic relations.

@@ Line 11: / Line 11: @@
 # The geometric language of sets
-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.
+Thus, one way to explain the relationships that hold among these concepts is to describe the ''translations'' that are induced among the allied families of notation.
 ===Syntactic Transformation Rules===

@@ Line 3: / Line 3: @@
 <div class="nonumtoc">__TOC__</div>
-==Syntactic Transformations==
+====1.3.12.  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.
+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:
-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 functional language of propositions
 ===Syntactic Transformation Rules===

@@ Line 446: / Line 446: @@
 |}
-'''Editing Note.'''  The last draft I can find has 5 variants of the next box, for "Value&nbsp;Rule&nbsp;1", and I can't tell right off which I meant to use.  Until I can get back to this, here's a link to the collection of variants:
+'''Editing Note.'''  The last draft I can find has 5 variants for the next box, "Value&nbsp;Rule&nbsp;1", and I can't tell right off which I meant to use.  Until I can get back to this, here's a link to the collection of variants:
 * [http://mywikibiz.com/User:Jon_Awbrey/SCRATCHPAD#Value_Rule_1 Value Rule 1]

@@ Line 432: / Line 432: @@
 '''Editing Note.'''  Need a transition here.  Give a brief description of the Tables of Translation Rules that have now been moved to the Appendices, and then move on to the rest of the Definitions and Proof Schemata.
 A rule that allows one to turn equivalent sentences into identical propositions:
-(S <=> T) <=> ([S] = [T])
+{| align="center" cellpadding="8" width="90%"
+| <math>(S \Leftrightarrow T) \quad \Leftrightarrow \quad (\downharpoonleft S \downharpoonright = \downharpoonleft T \downharpoonright)</math>
-Consider [ v = w ](v, w) and [ v(u) = w(u) ](u)
+|}
-then the following are identical propositions on U:
+Compare:
-V1a.	[ f = g ]
+{| align="center" cellpadding="8" width="90%"
-V1b.	[ f <=> g ]
+'''Editing Note.'''  The last draft that I can find has 5 variants of the next box, for "Value&nbsp;Rule&nbsp;1", and I can't right off which one I meant to use.  Until I can get back to this, here is a link to the collection of variants:
-V1c.	(( f , g ))$
+* [http://mywikibiz.com/User:Jon_Awbrey/SCRATCHPAD#Value_Rule_1 Value Rule 1]
 <br>