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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)

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→‎6.11. Higher Order Sign Relations : Application: markup

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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:

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# The variable name <math>{}^{\backprime\backprime} q {}^{\prime\prime}</math> is a HA sign that makes a PIR to the elements of <math>S.\!</math>

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# The variable name <math>{}^{\backprime\backprime} L {}^{\prime\prime}</math> is a HU sign that makes a PIR to the elements of <math>\{ L(\text{A}), L(\text{B}) \}.\!</math>

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# The constant name <math>{}^{\backprime\backprime} L(\text{A}) {}^{\prime\prime}</math> is a HI sign that makes a PIR to the elements of <math>L(\text{A}).\!</math>

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# The constant name <math>{}^{\backprime\backprime} L(\text{B}) {}^{\prime\prime}</math> is a HI sign that makes a PIR to the elements of <math>L(\text{B}).\!</math>

<pre>

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~~# The variable name <math>q\!</math> is a HA sign that makes a PIR to the elements of <math>S.\!</math>~~

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~~# The variable name "L" is a HU sign that makes a PIR to the elements of <math>\{ L(\text{A}), L(\text{B}) \}.\!</math>~~

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~~# The constant name "L(A)" is a HI sign that makes a PIR to the elements of <math>L(\text{A}).\!</math>~~

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~~# The constant name "L(B)" is a HI sign that makes a PIR to the elements of <math>L(\text{B}).\!</math>~~

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This results in a HO sign relation for QAB that is shown in Table 46.

Jon Awbrey

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