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Directory talk:Jon Awbrey/Papers/Inquiry Driven Systems : Part 1 (view source)

Revision as of 19:54, 14 September 2010

2,081 bytes added ,  19:54, 14 September 2010
→‎1.3.4.2. Sign Relations : A Primer
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In the present example, <math>S = I = \text{Syntactic Domain}</math>.
 
In the present example, <math>S = I = \text{Syntactic Domain}</math>.
   −
The sign relation associated with a given interpreter ''J'' is denoted ''L''<sub>''J''&nbsp;</sub> or ''L''(''J'').  Tables&nbsp;1 and 2 give the sign relations associated with the interpreters ''A'' and ''B'', respectively, putting them in the form of ''[[relational database]]s''.  Thus, the rows of each Table list the ordered triples of the form ‹''o'',&nbsp;''s'',&nbsp;''i''› that make up the corresponding sign relations, ''L''<sub>''A''&nbsp;</sub>,&nbsp;''L''<sub>''B''&nbsp;</sub>&nbsp;&sube;&nbsp;''O''&nbsp;&times;&nbsp;''S''&nbsp;&times;&nbsp;''I''.  It is often tempting to use the same names for objects and for relations involving these objects, but it is best to avoid this in a first approach, taking up the issues that this practice raises after the less problematic features of these relations have been treated.
+
The sign relation associated with a given interpreter <math>J\!</math> is denoted <math>L_J</math> or <math>L(J)</math>.  Tables&nbsp;1 and 2 give the sign relations associated with the interpreters <math>\text{A}</math> and <math>\text{B}</math>, respectively, putting them in the form of ''[[relational database]]s''.  Thus, the rows of each Table list the ordered triples of the form <math>(o, s, i)</math> that make up the corresponding sign relations, <math>L_\text{A}, L_\text{B} \subseteq</math><math>O \times S \times I</math>.  It is often tempting to use the same names for objects and for relations involving these objects, but it is best to avoid this in a first approach, taking up the issues that this practice raises after the less problematic features of these relations have been treated.
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{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:60%"
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<br>
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|+ Table 1. Sign Relation of Interpreter ''A''
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|- style="background:paleturquoise"
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{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:80%"
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! style="width:20%" | Object
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|+ style="height:30px" | <math>\text{Table 1.} ~~ \text{Sign Relation of Interpreter A}</math>
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! style="width:20%" | Sign
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|- style="height:40px; background:#f0f0ff"
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! style="width:20%" | Interpretant
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| <math>\text{Object}</math>
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|-
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| <math>\text{Sign}</math>
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| ''A'' || "A" || "A"
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| <math>\text{Interpretant}</math>
−
|-
  −
| ''A'' || "A" || "i"
  −
|-
  −
| ''A'' || "i" || "A"
  −
|-
  −
| ''A'' || "i" || "i"
  −
|-
  −
| ''B'' || "B" || "B"
  −
|-
  −
| ''B'' || "B" || "u"
   
|-
 
|-
−
| ''B'' || "u" || "B"
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|
 +
<math>\begin{matrix}
 +
\text{A}
 +
\\
 +
\text{A}
 +
\\
 +
\text{A}
 +
\\
 +
\text{A}
 +
\end{matrix}</math>
 +
|
 +
<math>\begin{matrix}
 +
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
 +
\\
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{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
 +
\\
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{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
 +
\\
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{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
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\end{matrix}</math>
 +
|
 +
<math>\begin{matrix}
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{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
 +
\\
 +
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
 +
\\
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{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
 +
\\
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{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
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\end{matrix}</math>
 
|-
 
|-
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| ''B'' || "u" || "u"
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|
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<math>\begin{matrix}
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\text{B}
 +
\\
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\text{B}
 +
\\
 +
\text{B}
 +
\\
 +
\text{B}
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\end{matrix}</math>
 +
|
 +
<math>\begin{matrix}
 +
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
 +
\\
 +
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
 +
\\
 +
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
 +
\\
 +
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
 +
\end{matrix}</math>
 +
|
 +
<math>\begin{matrix}
 +
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
 +
\\
 +
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
 +
\\
 +
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
 +
\\
 +
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
 +
\end{matrix}</math>
 
|}
 
|}
 +
 
<br>
 
<br>
   −
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:60%"
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{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:80%"
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|+ Table 2. Sign Relation of Interpreter ''B''
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|+ style="height:30px" | <math>\text{Table 2.} ~~ \text{Sign Relation of Interpreter B}</math>
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|- style="background:paleturquoise"
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|- style="height:40px; background:#f0f0ff"
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! style="width:20%" | Object
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| <math>\text{Object}</math>
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! style="width:20%" | Sign
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| <math>\text{Sign}</math>
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! style="width:20%" | Interpretant
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| <math>\text{Interpretant}</math>
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|-
  −
| ''A'' || "A" || "A"
  −
|-
  −
| ''A'' || "A" || "u"
  −
|-
  −
| ''A'' || "u" || "A"
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|-
  −
| ''A'' || "u" || "u"
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|-
  −
| ''B'' || "B" || "B"
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|-
  −
| ''B'' || "B" || "i"
   
|-
 
|-
−
| ''B'' || "i" || "B"
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|
 +
<math>\begin{matrix}
 +
\text{A}
 +
\\
 +
\text{A}
 +
\\
 +
\text{A}
 +
\\
 +
\text{A}
 +
\end{matrix}</math>
 +
|
 +
<math>\begin{matrix}
 +
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
 +
\\
 +
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
 +
\\
 +
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
 +
\\
 +
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
 +
\end{matrix}</math>
 +
|
 +
<math>\begin{matrix}
 +
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
 +
\\
 +
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
 +
\\
 +
{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
 +
\\
 +
{}^{\backprime\backprime} \text{u} {}^{\prime\prime}
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\end{matrix}</math>
 
|-
 
|-
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| ''B'' || "i" || "i"
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|
 +
<math>\begin{matrix}
 +
\text{B}
 +
\\
 +
\text{B}
 +
\\
 +
\text{B}
 +
\\
 +
\text{B}
 +
\end{matrix}</math>
 +
|
 +
<math>\begin{matrix}
 +
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
 +
\\
 +
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
 +
\\
 +
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
 +
\\
 +
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
 +
\end{matrix}</math>
 +
|
 +
<math>\begin{matrix}
 +
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
 +
\\
 +
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
 +
\\
 +
{}^{\backprime\backprime} \text{B} {}^{\prime\prime}
 +
\\
 +
{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
 +
\end{matrix}</math>
 
|}
 
|}
 +
 
<br>
 
<br>
  
Jon Awbrey
12,080

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