Directory talk:Jon Awbrey/Papers/Differential Propositional Calculus - Revision history

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Jon Awbrey: Move [Expository Examples] to Talk Page

2011-12-27T04:22:50Z

Move [Expository Examples] to Talk Page

Jon Awbrey: TOC

2011-12-27T03:55:13Z

__TOC__

Jon Awbrey: delete obsolete note

2011-12-27T03:45:59Z

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MyWikiBiz: Number 1 on Yahoo!

2008-11-21T18:21:00Z

Number 1 on Yahoo!

Jon Awbrey: /* Elegant Graveyard */

2008-07-08T19:20:21Z

Elegant Graveyard

Jon Awbrey: /* Current Version @ PlanetMath : TeX Format */ update

2008-07-08T18:20:20Z

Current Version @ PlanetMath : TeX Format: update

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@@ Line 10,888: / Line 10,888: @@
 ===Tangent Operator===
 [[Category:Artificial Intelligence]]
 [[Category:Boolean Algebra]]
@@ Line 10,897: / Line 10,898: @@
 [[Category:Cybernetics]]
 [[Category:Differential Logic]]
 [[Category:Equational Reasoning]]
 [[Category:Formal Languages]]
 [[Category:Formal Systems]]
 [[Category:Graph Theory]]
 [[Category:Inquiry]]
 [[Category:Inquiry Driven Systems]]
 [[Category:Knowledge Representation]]
 [[Category:Logic]]
 [[Category:Logical Graphs]]
 [[Category:Mathematics]]
 [[Category:Philosophy]]
 [[Category:Propositional Calculus]]
 [[Category:Semiotics]]
 [[Category:Visualization]]

← Older revision		Revision as of 04:22, 27 December 2011
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	__TOC__		__TOC__
		+
		+	=Work In Progress=
		+
		+	==4. Expository Examples==
		+
		+	'''(Work In Progress)'''
		+
		+	Consider the logical proposition represented by the following venn diagram:
		+
		+	<center><pre>
		+	o-----------------------------------------------------------o
		+	\| X . . . . . . . . . . . . . . . . . . . . . . . . . . . . \|
		+	\| . . . . . . . . . . . . . . . . . . . . . . . . . . . . . \|
		+	\| . . . . . . . . . . .o-------------o. . . . . . . . . . . \|
		+	\| . . . . . . . . . . / . . . . . . . \ . . . . . . . . . . \|
		+	\| . . . . . . . . . ./. . . . . . . . .\. . . . . . . . . . \|
		+	\| . . . . . . . . . / . . . . . . . . . \ . . . . . . . . . \|
		+	\| . . . . . . . . ./. . . . . . . . . . .\. . . . . . . . . \|
		+	\| . . . . . . . . / . . . . . . . . . . . \ . . . . . . . . \|
		+	\| . . . . . . . .o. . . . . . . . . . . . .o. . . . . . . . \|
		+	\| . . . . . . . .\|. . . . . . U . . . . . .\|. . . . . . . . \|
		+	\| . . . . . . . .\|. . . . . . . . . . . . .\|. . . . . . . . \|
		+	\| . . . . . . . .\|. . . . . . . . . . . . .\|. . . . . . . . \|
		+	\| . . . . . . . .\|. . . . . . . . . . . . .\|. . . . . . . . \|
		+	\| . . . . . . . .\|. . . . . . . . . . . . .\|. . . . . . . . \|
		+	\| . . . . . . o--o----------o . o----------o--o . . . . . . \|
		+	\| . . . . . ./. . \%%%%%%%%%%\./%%%%%%%%%%/ . .\. . . . . . \|
		+	\| . . . . . / . . .\%%%%%%%%%%o%%%%%%%%%%/. . . \ . . . . . \|
		+	\| . . . . ./. . . . \%%%%%%%%/%\%%%%%%%%/ . . . .\. . . . . \|
		+	\| . . . . / . . . . .\%%%%%%/%%%\%%%%%%/. . . . . \ . . . . \|
		+	\| . . . ./. . . . . . \%%%%/%%%%%\%%%%/ . . . . . .\. . . . \|
		+	\| . . . o . . . . . . .o--o-------o--o. . . . . . . o . . . \|
		+	\| . . . \| . . . . . . . . \|%%%%%%%\| . . . . . . . . \| . . . \|
		+	\| . . . \| . . . . . . . . \|%%%%%%%\| . . . . . . . . \| . . . \|
		+	\| . . . \| . . . . . . . . \|%%%%%%%\| . . . . . . . . \| . . . \|
		+	\| . . . \| . . . .V. . . . \|%%%%%%%\| . . . .W. . . . \| . . . \|
		+	\| . . . \| . . . . . . . . \|%%%%%%%\| . . . . . . . . \| . . . \|
		+	\| . . . o . . . . . . . . o%%%%%%%o . . . . . . . . o . . . \|
		+	\| . . . .\. . . . . . . . .\%%%%%/. . . . . . . . ./. . . . \|
		+	\| . . . . \ . . . . . . . . \%%%/ . . . . . . . . / . . . . \|
		+	\| . . . . .\. . . . . . . . .\%/. . . . . . . . ./. . . . . \|
		+	\| . . . . . \ . . . . . . . . o . . . . . . . . / . . . . . \|
		+	\| . . . . . .\. . . . . . . ./.\. . . . . . . ./. . . . . . \|
		+	\| . . . . . . o-------------o . o-------------o . . . . . . \|
		+	\| . . . . . . . . . . . . . . . . . . . . . . . . . . . . . \|
		+	\| . . . . . . . . . . . . . . . . . . . . . . . . . . . . . \|
		+	o-----------------------------------------------------------o
		+	</pre>
		+	'''Figure 1. Proposition''' <math>q : X \to \mathbb{B}</math>
		+	</center>
		+
		+	The following language is useful in describing the facts represented by the venn diagram.
		+
		+	* The universe of discourse is a set, <math>X,\!</math> represented by the area inside the large rectangle.
		+
		+	* The boolean domain is a set of two elements, <math>\mathbb{B} = \{ 0, 1 \},</math> represented by the two distinct shadings of the regions inside the rectangle.
		+
		+	* According to the conventions observed in this context, the algebraic value 0 is interpreted as the logical value <math>\operatorname{false}</math> and represented by the lighter shading, while the algebraic value 1 is interpreted as the logical value <math>\operatorname{true}</math> and represented by the darker shading.
		+
		+	* The universe of discourse <math>X\!</math> is the domain of three functions <math>u, v, w : X \to \mathbb{B}</math> called ''basic'', ''coordinate'', or ''simple'' propositions.
		+
		+	* As with any proposition, <math>p : X \to \mathbb{B},</math> a simple proposition partitions <math>X\!</math> into two fibers, the fiber of 0 under <math>p,\!</math> defined as <math>p^{-1}(0) \subseteq X,</math> and the fiber of 1 under <math>p,\!</math> defined as <math>p^{-1}(1) \subseteq X.</math>
		+
		+	* Each coordinate proposition is represented by a "circle", or a simple closed curve, that divides the rectangular region into the region exterior to the circle, representing the fiber of 0 under <math>p,\!</math> and the region interior to the circle, representing the fiber of 1 under <math>p.\!</math>
		+
		+	* The fibers of 1 under the propositions <math>u, v, w\!</math> are the respective subsets <math>U, V, W \subseteq X.</math>
		+
		+	'''…'''

	=Material To Be Collated=		=Material To Be Collated=

← Older revision		Revision as of 03:55, 27 December 2011
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		+	__TOC__
		+
	=Material To Be Collated=		=Material To Be Collated=

← Older revision		Revision as of 03:45, 27 December 2011
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	===Tangent Operator===		===Tangent Operator===
−
−	~~=Search Result=~~
−
−	Jon, it came to my attention from site traffic data that this page is the '''Number 1 Result''' on Yahoo! for [http://search.yahoo.com/search;_ylt=A0oGkkhtoiZJEA0BXnlXNyoA?fr2=sg-gac&sado=1&p=calculus%20differential%20table&fr=yfp-t-501&ei=UTF-8&fp_ip=PH&rd=r1&meta=vc%3Dph calculus differential table]. One notch higher than Wikipedia. Yay! (Feel free to delete or move this note, if it's interfering with your work below.) — [[User:MyWikiBiz\|MyWikiBiz]] 10:21, 21 November 2008 (PST)

← Older revision		Revision as of 18:21, 21 November 2008
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		+	==Search result==
		+	Jon, it came to my attention from site traffic data that this page is the '''# 1 result''' on Yahoo! for [http://search.yahoo.com/search;_ylt=A0oGkkhtoiZJEA0BXnlXNyoA?fr2=sg-gac&sado=1&p=calculus%20differential%20table&fr=yfp-t-501&ei=UTF-8&fp_ip=PH&rd=r1&meta=vc%3Dph calculus differential table]. One notch higher than Wikipedia. Yay! (Feel free to delete or move this note, if it's interfering with your work below.) -- [[User:MyWikiBiz\|MyWikiBiz]] 10:21, 21 November 2008 (PST)
		+
	__TOC__		__TOC__

← Older revision		Revision as of 19:20, 8 July 2008
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	Up to this point we have been treating the universe of discourse <math>X,\!</math> the quality <math>q,\!</math> and the symbol "<math>q\!</math>" as all of one piece, almost as if the entire context marked by <math>X\!</math> and <math>q\!</math> and "<math>q\!</math>" amounted to the only way of viewing <math>X.\!</math> That is clearly not the case, but the fact is that people often use the term "universe of discourse" to cover a particular set of distinctions drawn in the space <math>X\!</math> and even sometimes a particular calculus or language for discussing the elements of <math>X.\!</math> If it were possible to coin a new phrase in this realm one might distinguish these latter components as the "discursive universe", but there is probably no escape from simply recognizing the equivocal senses of the terms already in use and trying to clarify the senses intended in context.		Up to this point we have been treating the universe of discourse <math>X,\!</math> the quality <math>q,\!</math> and the symbol "<math>q\!</math>" as all of one piece, almost as if the entire context marked by <math>X\!</math> and <math>q\!</math> and "<math>q\!</math>" amounted to the only way of viewing <math>X.\!</math> That is clearly not the case, but the fact is that people often use the term "universe of discourse" to cover a particular set of distinctions drawn in the space <math>X\!</math> and even sometimes a particular calculus or language for discussing the elements of <math>X.\!</math> If it were possible to coin a new phrase in this realm one might distinguish these latter components as the "discursive universe", but there is probably no escape from simply recognizing the equivocal senses of the terms already in use and trying to clarify the senses intended in context.
		+
		+	'''…'''
		+
		+	Suppose we discover or begin to suspect that something we had been treating as a simple quality, <math>q,\!</math> is actually compounded of other qualities, <math>u\!</math> and <math>v\!</math>, according to a propositional formula <math>q = q(u, v).\!</math>

	'''…'''		'''…'''

Directory talk:Jon Awbrey/Papers/Differential Propositional Calculus - Revision history

Jon Awbrey: delete old PlanetMath TeX and move remainder to Directory:Jon Awbrey/Differential Logic : Various_Sketches

Jon Awbrey: add cats

Jon Awbrey: sub \mathrm for \operatorname

Jon Awbrey: Move [Expository Examples] to Talk Page

Jon Awbrey: __TOC__

Jon Awbrey: delete obsolete note

Jon Awbrey: Move “Material To Be Collated” to Talk Page

MyWikiBiz: Number 1 on Yahoo!

Jon Awbrey: /* Elegant Graveyard */

Jon Awbrey: /* Current Version @ PlanetMath : TeX Format */ update

Jon Awbrey: TOC