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Revision as of 19:54, 14 September 2010
, 19:54, 14 September 2010→1.3.4.2. Sign Relations : A Primer
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−! style="width:20%" | Object+! style="width:20%" | Sign+! style="width:20%" | Interpretant+|-+| ''A'' || "A" || "A"+|-
−| ''A'' || "A" || "i"
−|-
−| ''A'' || "i" || "A"
−|-
−| ''A'' || "i" || "i"
−|-
−| ''B'' || "B" || "B"
−|-
−| ''B'' || "B" || "u"
! style="width:20%" | Object+! style="width:20%" | Sign+! style="width:20%" | Interpretant+|-
−| ''A'' || "A" || "A"
−|-
−| ''A'' || "A" || "u"
−|-
−| ''A'' || "u" || "A"
−|-
−| ''A'' || "u" || "u"
−|-
−| ''B'' || "B" || "B"
−|-
−| ''B'' || "B" || "i"
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'' </sub> or ''L''(''J''). Tables 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'', ''s'', ''i''› that make up the corresponding sign relations, ''L''<sub>''A'' </sub>, ''L''<sub>''B'' </sub> ⊆ ''O'' × ''S'' × ''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 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.
−{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:60%"
+<br>
−|+ Table 1. Sign Relation of Interpreter ''A''
+|- style="background:paleturquoise"
+{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:80%"
−|+ style="height:30px" | <math>\text{Table 1.} ~~ \text{Sign Relation of Interpreter A}</math>
−|- style="height:40px; background:#f0f0ff"
−| <math>\text{Object}</math>
−| <math>\text{Sign}</math>
−| <math>\text{Interpretant}</math>
−|-
|-
−| ''B'' || "u" || "B"
+|
+<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{i} {}^{\prime\prime}
+\\
+{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
+\end{matrix}</math>
+|
+<math>\begin{matrix}
+{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
+\\
+{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
+\\
+{}^{\backprime\backprime} \text{A} {}^{\prime\prime}
+\\
+{}^{\backprime\backprime} \text{i} {}^{\prime\prime}
+\end{matrix}</math>
|-
|-
−| ''B'' || "u" || "u"
+|
+<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{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%"
+{| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:80%"
−|+ Table 2. Sign Relation of Interpreter ''B''
+|+ style="height:30px" | <math>\text{Table 2.} ~~ \text{Sign Relation of Interpreter B}</math>
−|- style="background:paleturquoise"
+|- style="height:40px; background:#f0f0ff"
−| <math>\text{Object}</math>
−| <math>\text{Sign}</math>
−| <math>\text{Interpretant}</math>
−|-
|-
−| ''B'' || "i" || "B"
+|
+<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}
+\end{matrix}</math>
|-
|-
−| ''B'' || "i" || "i"
+|
+<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>
