Directory talk:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 - Revision history

Jon Awbrey: MathJaX SuX ❢❢❢

2014-08-28T18:21:08Z

MathJaX SuX ❢❢❢

Jon Awbrey at 18:19, 28 August 2014

2014-08-28T18:19:22Z

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Jon Awbrey: MathJaX SuX ❢❢❢

2014-08-28T18:02:02Z

MathJaX SuX ❢❢❢

Jon Awbrey: /* Current Work */

2013-05-18T02:40:24Z

Current Work

Jon Awbrey: /* Current Work */

2013-05-18T02:34:34Z

Current Work

Jon Awbrey: /* 1.3.4.3. Semiotic Equivalence Relations */

2013-05-18T02:12:35Z

1.3.4.3. Semiotic Equivalence Relations

Jon Awbrey: /* Current Work */

2013-05-18T02:05:03Z

Current Work

Jon Awbrey: /* Current Work */

2013-05-18T02:00:16Z

Current Work

Jon Awbrey: /* Current Work */

2013-05-16T02:18:14Z

Current Work

Jon Awbrey: /* Current Work */

2013-05-16T02:14:34Z

Current Work

← Older revision		Revision as of 18:21, 28 August 2014
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−	<p align="center"><font face="curlz mt" size="7">'''MathJaX ~~SuXs~~ ❢❢❢'''</font></p>	+	<p align="center"><font face="curlz mt" size="7">'''MathJaX SuX ❢❢❢'''</font></p>

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

← Older revision		Revision as of 18:02, 28 August 2014
Line 1:		Line 1:
		+	'''MathJaX SuXs ❢❢❢'''
		+
	<div class="nonumtoc">__TOC__</div>		<div class="nonumtoc">__TOC__</div>
		+
		+	'''NOTE. I am putting the last few Sections of Part 6 here until I can figure out why the article page is not rendering the full amount of edit page text that it used to show.'''
		+
		+	==6. Reflective Interpretive Frameworks (cont.)==

	==Deletions==		==Deletions==

← Older revision		Revision as of 02:40, 18 May 2013
Line 9,093:		Line 9,093:

	==Current Work==		==Current Work==
−
−	~~<br>~~
−
−	~~The semiotic equivalence relation given by <math>\operatorname{Con}^1 (L_\text{A})\!</math> for interpreter <math>\text{A}\!</math> has the following semiotic equations.~~
−
−	~~{\| cellpadding="10"~~
−	~~\| width="10%" \|  ~~
−	~~\| <math>[ {}^{\langle} \text{A} {}^{\rangle} ]_\text{A}\!</math>~~
−	~~\| <math>=\!</math>~~
−	~~\| <math>[ {}^{\langle} \text{i} {}^{\rangle} ]_\text{A}\!</math>~~
−	~~\| width="20%" \|  ~~
−	~~\| <math>[ {}^{\langle} \text{B} {}^{\rangle} ]_\text{A}\!</math>~~
−	~~\| <math>=\!</math>~~
−	~~\| <math>[ {}^{\langle} \text{u} {}^{\rangle} ]_\text{A}\!</math>~~
−	\|-
−	~~\| width="10%" \| or~~
−	~~\|  <math>{}^{\langle} \text{A} {}^{\rangle}\!</math>~~
−	~~\| <math>=_\text{A}\!</math>~~
−	~~\|  <math>{}^{\langle} \text{i} {}^{\rangle}\!</math>~~
−	~~\| width="20%" \|  ~~
−	~~\|  <math>{}^{\langle} \text{B} {}^{\rangle}\!</math>~~
−	~~\| <math>=_\text{A}\!</math>~~
−	~~\|  <math>{}^{\langle} \text{u} {}^{\rangle}\!</math>~~
−	\|}
−
−	~~These equations induce the following semiotic partition.~~
−
−	~~{\| align="center" cellspacing="6" width="90%"~~
−	\|
−	~~<math>~~
−	\{
−	~~\{ {}^{\langle} \text{A} {}^{\rangle}, {}^{\langle} \text{i} {}^{\rangle} \},~~
−	~~\{ {}^{\langle} \text{B} {}^{\rangle}, {}^{\langle} \text{u} {}^{\rangle} \},~~
−	~~\{ {}^{\langle\langle} \text{A} {}^{\rangle\rangle} \},~~
−	~~\{ {}^{\langle\langle} \text{i} {}^{\rangle\rangle} \},~~
−	~~\{ {}^{\langle\langle} \text{B} {}^{\rangle\rangle} \},~~
−	~~\{ {}^{\langle\langle} \text{u} {}^{\rangle\rangle} \}~~
−	~~\}.\!~~
−	~~</math>~~
−	\|}
−
−	~~The semiotic equivalence relation given by <math>\operatorname{Con}^1 (L_\text{B})\!</math> for interpreter <math>\text{B}\!</math> has the following semiotic equations.~~
−
−	~~{\| cellpadding="10"~~
−	~~\| width="10%" \|  ~~
−	~~\| <math>[ {}^{\langle} \text{A} {}^{\rangle} ]_\text{B}\!</math>~~
−	~~\| <math>=\!</math>~~
−	~~\| <math>[ {}^{\langle} \text{u} {}^{\rangle} ]_\text{B}\!</math>~~
−	~~\| width="20%" \|  ~~
−	~~\| <math>[ {}^{\langle} \text{B} {}^{\rangle} ]_\text{B}\!</math>~~
−	~~\| <math>=\!</math>~~
−	~~\| <math>[ {}^{\langle} \text{i} {}^{\rangle} ]_\text{B}\!</math>~~
−	\|-
−	~~\| width="10%" \| or~~
−	~~\|  <math>{}^{\langle} \text{A} {}^{\rangle}\!</math>~~
−	~~\| <math>=_\text{B}\!</math>~~
−	~~\|  <math>{}^{\langle} \text{u} {}^{\rangle}\!</math>~~
−	~~\| width="20%" \|  ~~
−	~~\|  <math>{}^{\langle} \text{B} {}^{\rangle}\!</math>~~
−	~~\| <math>=_\text{B}\!</math>~~
−	~~\|  <math>{}^{\langle} \text{i} {}^{\rangle}\!</math>~~
−	\|}
−
−	~~These equations induce the following semiotic partition.~~
−
−	~~{\| align="center" cellspacing="6" width="90%"~~
−	\|
−	~~<math>~~
−	\{
−	~~\{ {}^{\langle} \text{A} {}^{\rangle}, {}^{\langle} \text{u} {}^{\rangle} \},~~
−	~~\{ {}^{\langle} \text{B} {}^{\rangle}, {}^{\langle} \text{i} {}^{\rangle} \},~~
−	~~\{ {}^{\langle\langle} \text{A} {}^{\rangle\rangle} \},~~
−	~~\{ {}^{\langle\langle} \text{i} {}^{\rangle\rangle} \},~~
−	~~\{ {}^{\langle\langle} \text{B} {}^{\rangle\rangle} \},~~
−	~~\{ {}^{\langle\langle} \text{u} {}^{\rangle\rangle} \}~~
−	~~\}.\!~~
−	~~</math>~~
−	\|}

	<br>		<br>

@@ Line 9,100: / Line 9,100: @@
 {| cellpadding="10"
 | width="10%" | &nbsp;
-| <math>[{}^{\backprime\backprime} \text{A} {}^{\prime\prime}]_\text{A}\!</math>
+| <math>[ {}^{\langle} \text{A} {}^{\rangle} ]_\text{A}\!</math>
 | <math>=\!</math>
-| <math>[{}^{\backprime\backprime} \text{i} {}^{\prime\prime}]_\text{A}\!</math>
+| <math>[ {}^{\langle} \text{i} {}^{\rangle} ]_\text{A}\!</math>
 | width="20%" | &nbsp;
-| <math>[{}^{\backprime\backprime} \text{B} {}^{\prime\prime}]_\text{A}\!</math>
+| <math>[ {}^{\langle} \text{B} {}^{\rangle} ]_\text{A}\!</math>
 | <math>=\!</math>
-| <math>[{}^{\backprime\backprime} \text{u} {}^{\prime\prime}]_\text{A}\!</math>
+| <math>[ {}^{\langle} \text{u} {}^{\rangle} ]_\text{A}\!</math>
 |-
 | width="10%" | or
-| &nbsp;<math>{}^{\backprime\backprime} \text{A} {}^{\prime\prime}\!</math>
+| &nbsp;<math>{}^{\langle} \text{A} {}^{\rangle}\!</math>
 | <math>=_\text{A}\!</math>
-| &nbsp;<math>{}^{\backprime\backprime} \text{i} {}^{\prime\prime}\!</math>
+| &nbsp;<math>{}^{\langle} \text{i} {}^{\rangle}\!</math>
 | width="20%" | &nbsp;
-| &nbsp;<math>{}^{\backprime\backprime} \text{B} {}^{\prime\prime}\!</math>
+| &nbsp;<math>{}^{\langle} \text{B} {}^{\rangle}\!</math>
 | <math>=_\text{A}\!</math>
-| &nbsp;<math>{}^{\backprime\backprime} \text{u} {}^{\prime\prime}\!</math>
+| &nbsp;<math>{}^{\langle} \text{u} {}^{\rangle}\!</math>
 |}
-and the semiotic partition:  <math>\{ \{ {}^{\backprime\backprime} \text{A} {}^{\prime\prime}, {}^{\backprime\backprime} \text{i} {}^{\prime\prime} \} , \{ {}^{\backprime\backprime} \text{B} {}^{\prime\prime}, {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \} \}\!</math>.
+These equations induce the following semiotic partition.
 The semiotic equivalence relation given by <math>\operatorname{Con}^1 (L_\text{B})\!</math> for interpreter <math>\text{B}\!</math> has the following semiotic equations.
@@ Line 9,124: / Line 9,138: @@
 {| cellpadding="10"
 | width="10%" | &nbsp;
-| <math>[{}^{\backprime\backprime} \text{A} {}^{\prime\prime}]_\text{B}\!</math>
+| <math>[ {}^{\langle} \text{A} {}^{\rangle} ]_\text{B}\!</math>
 | <math>=\!</math>
-| <math>[{}^{\backprime\backprime} \text{u} {}^{\prime\prime}]_\text{B}\!</math>
+| <math>[ {}^{\langle} \text{u} {}^{\rangle} ]_\text{B}\!</math>
 | width="20%" | &nbsp;
-| <math>[{}^{\backprime\backprime} \text{B} {}^{\prime\prime}]_\text{B}\!</math>
+| <math>[ {}^{\langle} \text{B} {}^{\rangle} ]_\text{B}\!</math>
 | <math>=\!</math>
-| <math>[{}^{\backprime\backprime} \text{i} {}^{\prime\prime}]_\text{B}\!</math>
+| <math>[ {}^{\langle} \text{i} {}^{\rangle} ]_\text{B}\!</math>
 |-
 | width="10%" | or
-| &nbsp;<math>{}^{\backprime\backprime} \text{A} {}^{\prime\prime}\!</math>
+| &nbsp;<math>{}^{\langle} \text{A} {}^{\rangle}\!</math>
 | <math>=_\text{B}\!</math>
-| &nbsp;<math>{}^{\backprime\backprime} \text{u} {}^{\prime\prime}\!</math>
+| &nbsp;<math>{}^{\langle} \text{u} {}^{\rangle}\!</math>
 | width="20%" | &nbsp;
-| &nbsp;<math>{}^{\backprime\backprime} \text{B} {}^{\prime\prime}\!</math>
+| &nbsp;<math>{}^{\langle} \text{B} {}^{\rangle}\!</math>
 | <math>=_\text{B}\!</math>
-| &nbsp;<math>{}^{\backprime\backprime} \text{i} {}^{\prime\prime}\!</math>
+| &nbsp;<math>{}^{\langle} \text{i} {}^{\rangle}\!</math>
 |}
-and the semiotic partition:  <math>\{ \{ {}^{\backprime\backprime} \text{A} {}^{\prime\prime}, {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \} , \{ {}^{\backprime\backprime} \text{B} {}^{\prime\prime}, {}^{\backprime\backprime} \text{i} {}^{\prime\prime} \} \}\!</math>.
+These equations induce the following semiotic partition.
 <br>

@@ Line 370: / Line 370: @@
 |}
-and the semiotic partition:  <math>\{ \{ {}^{\backprime\backprime} \text{A} {}^{\prime\prime}, {}^{\backprime\backprime} \text{i} {}^{\prime\prime} \} , \{ {}^{\backprime\backprime} \text{B} {}^{\prime\prime}, {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \} \}\!</math>.
+and the semiotic partition:  <math>\{ \{ {}^{\backprime\backprime} \text{A} {}^{\prime\prime}, {}^{\backprime\backprime} \text{i} {}^{\prime\prime} \} , \{ {}^{\backprime\backprime} \text{B} {}^{\prime\prime}, {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \} \}.\!</math>
 In contrast, the SER for interpreter <math>\text{B}\!</math> yields the semiotic equations:
@@ Line 394: / Line 394: @@
 |}
-and the semiotic partition:  <math>\{ \{ {}^{\backprime\backprime} \text{A} {}^{\prime\prime}, {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \} , \{ {}^{\backprime\backprime} \text{B} {}^{\prime\prime}, {}^{\backprime\backprime} \text{i} {}^{\prime\prime} \} \}\!</math>.
+and the semiotic partition:  <math>\{ \{ {}^{\backprime\backprime} \text{A} {}^{\prime\prime}, {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \} , \{ {}^{\backprime\backprime} \text{B} {}^{\prime\prime}, {}^{\backprime\backprime} \text{i} {}^{\prime\prime} \} \}.\!</math>
 <br>

← Older revision		Revision as of 02:00, 18 May 2013
Line 9,093:		Line 9,093:

	==Current Work==		==Current Work==
		+
		+	<br>
		+
		+	In these terms, the SER for interpreter <math>\text{A}\!</math> yields the semiotic equations:
		+
		+	{\| cellpadding="10"
		+	\| width="10%" \|
		+	\| <math>[{}^{\backprime\backprime} \text{A} {}^{\prime\prime}]_\text{A}\!</math>
		+	\| <math>=\!</math>
		+	\| <math>[{}^{\backprime\backprime} \text{i} {}^{\prime\prime}]_\text{A}\!</math>
		+	\| width="20%" \|
		+	\| <math>[{}^{\backprime\backprime} \text{B} {}^{\prime\prime}]_\text{A}\!</math>
		+	\| <math>=\!</math>
		+	\| <math>[{}^{\backprime\backprime} \text{u} {}^{\prime\prime}]_\text{A}\!</math>
		+	\|-
		+	\| width="10%" \| or
		+	\|  <math>{}^{\backprime\backprime} \text{A} {}^{\prime\prime}\!</math>
		+	\| <math>=_\text{A}\!</math>
		+	\|  <math>{}^{\backprime\backprime} \text{i} {}^{\prime\prime}\!</math>
		+	\| width="20%" \|
		+	\|  <math>{}^{\backprime\backprime} \text{B} {}^{\prime\prime}\!</math>
		+	\| <math>=_\text{A}\!</math>
		+	\|  <math>{}^{\backprime\backprime} \text{u} {}^{\prime\prime}\!</math>
		+	\|}
		+
		+	and the semiotic partition: <math>\{ \{ {}^{\backprime\backprime} \text{A} {}^{\prime\prime}, {}^{\backprime\backprime} \text{i} {}^{\prime\prime} \} , \{ {}^{\backprime\backprime} \text{B} {}^{\prime\prime}, {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \} \}\!</math>.
		+
		+	In contrast, the SER for interpreter <math>\text{B}\!</math> yields the semiotic equations:
		+
		+	{\| cellpadding="10"
		+	\| width="10%" \|
		+	\| <math>[{}^{\backprime\backprime} \text{A} {}^{\prime\prime}]_\text{B}\!</math>
		+	\| <math>=\!</math>
		+	\| <math>[{}^{\backprime\backprime} \text{u} {}^{\prime\prime}]_\text{B}\!</math>
		+	\| width="20%" \|
		+	\| <math>[{}^{\backprime\backprime} \text{B} {}^{\prime\prime}]_\text{B}\!</math>
		+	\| <math>=\!</math>
		+	\| <math>[{}^{\backprime\backprime} \text{i} {}^{\prime\prime}]_\text{B}\!</math>
		+	\|-
		+	\| width="10%" \| or
		+	\|  <math>{}^{\backprime\backprime} \text{A} {}^{\prime\prime}\!</math>
		+	\| <math>=_\text{B}\!</math>
		+	\|  <math>{}^{\backprime\backprime} \text{u} {}^{\prime\prime}\!</math>
		+	\| width="20%" \|
		+	\|  <math>{}^{\backprime\backprime} \text{B} {}^{\prime\prime}\!</math>
		+	\| <math>=_\text{B}\!</math>
		+	\|  <math>{}^{\backprime\backprime} \text{i} {}^{\prime\prime}\!</math>
		+	\|}
		+
		+	and the semiotic partition: <math>\{ \{ {}^{\backprime\backprime} \text{A} {}^{\prime\prime}, {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \} , \{ {}^{\backprime\backprime} \text{B} {}^{\prime\prime}, {}^{\backprime\backprime} \text{i} {}^{\prime\prime} \} \}\!</math>.

	<br>		<br>

← Older revision		Revision as of 02:18, 16 May 2013
Line 9,093:		Line 9,093:

	==Current Work==		==Current Work==
−
−	~~<br>~~
−
−	The connotative components <math>\operatorname{Con}^1 (L_\text{A})\!</math> and <math>\operatorname{Con}^1 (L_\text{B})\!</math> can be viewed as digraphs on the eight points of the syntactic domain <math>S.\!</math> The arcs of these digraphs are given as follows.
−
−	~~<ol>~~
−	<li><math>\operatorname{Con}^1 (L_\text{A})\!</math> inherits from <math>L_\text{A}\!</math> the structure of a semiotic equivalence relation on <math>S^{(1)},\!</math> having a sling on each point of <math>S^{(1)},\!</math> arcs in both directions between <math>{}^{\langle} \text{A} {}^{\rangle}\!</math> and <math>{}^{\langle} \text{i}{}^{\rangle},\!</math> and arcs in both directions between <math>{}^{\langle} \text{B} {}^{\rangle}\!</math> and <math>{}^{\langle} \text{u}{}^{\rangle}.\!</math> The reflective extension <math>\operatorname{Ref}^1 (L_\text{A})\!</math> adds a sling on each point of <math>S^{(2)},\!</math> creating a semiotic equivalence relation on <math>S.\!</math></li>
−
−	<li><math>\operatorname{Con}^1 (L_\text{B})\!</math> inherits from <math>L_\text{B}\!</math> the structure of a semiotic equivalence relation on <math>S^{(1)},\!</math> having a sling on each point of <math>S^{(1)},\!</math> arcs in both directions between <math>{}^{\langle} \text{A} {}^{\rangle}\!</math> and <math>{}^{\langle} \text{u}{}^{\rangle},\!</math> and arcs in both directions between <math>{}^{\langle} \text{B} {}^{\rangle}\!</math> and <math>{}^{\langle} \text{i}{}^{\rangle}.\!</math> The reflective extension <math>\operatorname{Ref}^1 (L_\text{B})\!</math> adds a sling on each point of <math>S^{(2)},\!</math> creating a semiotic equivalence relation on <math>S.\!</math></li>
−	~~</ol>~~
−
−	Taken as transition digraphs, <math>\operatorname{Con}^1 (L_\text{A})\!</math> and <math>\operatorname{Con}^1 (L_\text{B})\!</math> highlight the associations between signs in <math>\operatorname{Ref}^1 (L_\text{A})\!</math> and <math>\operatorname{Ref}^1 (L_\text{B}),\!</math> respectively.

	<br>		<br>

@@ Line 9,099: / Line 9,099: @@
 <ol>
-<li><math>\operatorname{Con}^1 (L_\text{A})\!</math> inherits from <math>L_\text{A}\!</math> the structure of a semiotic equivalence relation on <math>S^{(1)},\!</math> having a sling on each point of <math>S^{(1)},\!</math> arcs in both directions between <math>{}^{\langle} \text{A} {}^{\rangle}\!</math> and <math>{}^{\langle} \text{i}{}^{\rangle},\!</math> and arcs in both directions between <math>{}^{\langle} \text{B} {}^{\rangle}\!</math> and <math>{}^{\langle} \text{u}{}^{\rangle}.\!</math></li>  The reflective extension <math>\operatorname{Ref}^1 (L_\text{A})\!</math> adds a sling on each point of <math>S^{(2)},\!</math> creating a semiotic equivalence relation on <math>S.\!</math>
+<li><math>\operatorname{Con}^1 (L_\text{A})\!</math> inherits from <math>L_\text{A}\!</math> the structure of a semiotic equivalence relation on <math>S^{(1)},\!</math> having a sling on each point of <math>S^{(1)},\!</math> arcs in both directions between <math>{}^{\langle} \text{A} {}^{\rangle}\!</math> and <math>{}^{\langle} \text{i}{}^{\rangle},\!</math> and arcs in both directions between <math>{}^{\langle} \text{B} {}^{\rangle}\!</math> and <math>{}^{\langle} \text{u}{}^{\rangle}.\!</math>  The reflective extension <math>\operatorname{Ref}^1 (L_\text{A})\!</math> adds a sling on each point of <math>S^{(2)},\!</math> creating a semiotic equivalence relation on <math>S.\!</math></li>
-<li><math>\operatorname{Con}^1 (L_\text{B})\!</math> inherits from <math>L_\text{B}\!</math> the structure of a semiotic equivalence relation on <math>S^{(1)},\!</math> having a sling on each point of <math>S^{(1)},\!</math> arcs in both directions between <math>{}^{\langle} \text{A} {}^{\rangle}\!</math> and <math>{}^{\langle} \text{u}{}^{\rangle},\!</math> and arcs in both directions between <math>{}^{\langle} \text{B} {}^{\rangle}\!</math> and <math>{}^{\langle} \text{i}{}^{\rangle}.\!</math></li>  The reflective extension <math>\operatorname{Ref}^1 (L_\text{B})\!</math> adds a sling on each point of <math>S^{(2)},\!</math> creating a semiotic equivalence relation on <math>S.\!</math>
+<li><math>\operatorname{Con}^1 (L_\text{B})\!</math> inherits from <math>L_\text{B}\!</math> the structure of a semiotic equivalence relation on <math>S^{(1)},\!</math> having a sling on each point of <math>S^{(1)},\!</math> arcs in both directions between <math>{}^{\langle} \text{A} {}^{\rangle}\!</math> and <math>{}^{\langle} \text{u}{}^{\rangle},\!</math> and arcs in both directions between <math>{}^{\langle} \text{B} {}^{\rangle}\!</math> and <math>{}^{\langle} \text{i}{}^{\rangle}.\!</math>  The reflective extension <math>\operatorname{Ref}^1 (L_\text{B})\!</math> adds a sling on each point of <math>S^{(2)},\!</math> creating a semiotic equivalence relation on <math>S.\!</math></li>
 </ol>