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, 04:11, 23 May 2012→6.11. Higher Order Sign Relations : Application: markup
This is not the place to take up the possibility of an ideal, universal, or even a very comprehensive interpreter for the language indicated here, so I specialize the account to consider an interpreter <math>Q_{\text{AB}} = Q(\text{A}, \text{B})\!</math> that is competent to cover the initial level of reflections that arise from the dialogue of <math>\text{A}\!</math> and <math>\text{B}.\!</math>
This is not the place to take up the possibility of an ideal, universal, or even a very comprehensive interpreter for the language indicated here, so I specialize the account to consider an interpreter <math>Q_{\text{AB}} = Q(\text{A}, \text{B})\!</math> that is competent to cover the initial level of reflections that arise from the dialogue of <math>\text{A}\!</math> and <math>\text{B}.\!</math>
For the interpreter <math>Q_{\text{AB}},\!</math> the sign variable <math>q\!</math> need only range over the syntactic domain <math>S = \{ {}^{\backprime\backprime} \text{A} {}^{\prime\prime}, {}^{\backprime\backprime} \text{B} {}^{\prime\prime}, {}^{\backprime\backprime} \text{i} {}^{\prime\prime}, {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \}\!</math> and the relation variable <math>L\!</math> need only range over the set of sign relations <math>\{ L(\text{A}), L(\text{B}) \}.\!</math> These requirements can be accomplished as follows:
<pre>
<pre>
1. The variable name "q" is a HA sign that makes a PIR to the elements of S.
1. The variable name "q" is a HA sign that makes a PIR to the elements of S.
2. The variable name "R" is a HU sign that makes a PIR to the elements of O, regarded as sign relations.
2. The variable name "L" is a HU sign that makes a PIR to the elements of <math>\{ L(\text{A}), L(\text{B}) \}.\!</math>
3. The constant name "A" is a HI sign that makes a PIR to the elements of A.
3. The constant name "L(A)" is a HI sign that makes a PIR to the elements of <math>L(\text{A}).\!</math>
4. The constant name "B" is a HI sign that makes a PIR to the elements of B.
4. The constant name "L(B)" is a HI sign that makes a PIR to the elements of <math>L(\text{B}).\!</math>
This results in a HO sign relation for QAB that is shown in Table 46.
This results in a HO sign relation for QAB that is shown in Table 46.
