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

Revision as of 15:10, 17 April 2013

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→‎6.38. Considering the Source: markup
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<br>
 
<br>
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<pre>
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Thus informed, the semiotic equivalence relation for interpreter <math>\text{A}\!</math> yields the following semiotic equations.
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Thus informed, the SER for interpreter A yields the semantic equations:
     −
["A"A]A   =   ["A"B]A   =   ["i"A]A   =   ["u"B]A,
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{| cellpadding="10"
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| width="10%" | &nbsp;
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| <math>[{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{A}}]_\text{A}\!</math>
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| <math>=\!</math>
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| <math>[{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{B}}]_\text{A}\!</math>
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| <math>=\!</math>
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| <math>[{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{A}}]_\text{A}\!</math>
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| <math>=\!</math>
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| <math>[{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{B}}]_\text{A}\!</math>
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|-
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| width="10%" | or
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| &nbsp;<math>{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{A}}\!</math>
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| <math>=_\text{A}\!</math>
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| &nbsp;<math>{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{B}}\!</math>
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| <math>=_\text{A}\!</math>
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| &nbsp;<math>{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{A}}\!</math>
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| <math>=_\text{A}\!</math>
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| &nbsp;<math>{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{B}}\!</math>
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|}
   −
or "A"A    =A  "A"B    =A  "i"A    =A  "u"B.
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In comparison, the semiotic equivalence relation for interpreter <math>\text{B}\!</math> yields the following semiotic equations.
   −
In comparison, the SER for interpreter B yields the semantic equations:
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{| cellpadding="10"
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| width="10%" | &nbsp;
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["A"A]B   =   ["A"B]B   =   ["i"A]B   =   ["u"B]B,
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| <math>[{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{A}}]_\text{B}\!</math>
−
 
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| <math>=\!</math>
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or "A"A     =B   "A"B     =B   "i"A     =B   "u"B.
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| <math>[{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{B}}]_\text{B}\!</math>
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| <math>=\!</math>
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| <math>[{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{A}}]_\text{B}\!</math>
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| <math>=\!</math>
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| <math>[{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{B}}]_\text{B}\!</math>
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|-
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| width="10%" | or
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| &nbsp;<math>{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{A}}\!</math>
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| <math>=_\text{B}\!</math>
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| &nbsp;<math>{}^{\backprime\backprime} \text{A} {}^{\prime\prime\text{B}}\!</math>
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| <math>=_\text{B}\!</math>
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| &nbsp;<math>{}^{\backprime\backprime} \text{i} {}^{\prime\prime\text{A}}\!</math>
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| <math>=_\text{B}\!</math>
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| &nbsp;<math>{}^{\backprime\backprime} \text{u} {}^{\prime\prime\text{B}}\!</math>
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|}
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<pre>
 
Consequently, both SERs now induce the same semantic partition on S:
 
Consequently, both SERs now induce the same semantic partition on S:
  
Jon Awbrey
12,080

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