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Directory talk:Jon Awbrey/Papers/Inquiry Driven Systems : Part 1 (view source)
Revision as of 17:22, 15 September 2010
, 17:22, 15 September 2010→1.3.4.3. Semiotic Equivalence Relations
In these terms, the SER for interpreter <math>\text{A}</math> yields the semiotic equations:
In these terms, the SER for interpreter <math>\text{A}</math> yields the semiotic equations:
{| cellpadding=4 style="text-align:center"
{| cellpadding="10"
| align=left cellpadding=0 width=10% |
| width="10%" |
| ["A"]<sub>''A''</sub>
| <math>[{}^{\backprime\backprime} \text{A} {}^{\prime\prime}]_\text{A}</math>
| =
| <math>=</math>
| ["i"]<sub>''A''</sub>
| <math>[{}^{\backprime\backprime} \text{i} {}^{\prime\prime}]_\text{A}</math>
| ,
| width="20%" |
| ["B"]<sub>''A''</sub>
| <math>[{}^{\backprime\backprime} \text{B} {}^{\prime\prime}]_\text{A}</math>
| =
| <math>=</math>
| ["u"]<sub>''A''</sub>
| <math>[{}^{\backprime\backprime} \text{u} {}^{\prime\prime}]_\text{A}</math>
|-
|-
| align=left cellpadding=0 width=10% | or
| width="10%" | or
| "A"
| <math>{}^{\backprime\backprime} \text{A} {}^{\prime\prime}</math>
| =<sub>''A''</sub>
| <math>=_\text{A}</math>
| "i"
| <math>{}^{\backprime\backprime} \text{i} {}^{\prime\prime}</math>
| ,
| width="20%" |
| "B"
| <math>{}^{\backprime\backprime} \text{B} {}^{\prime\prime}</math>
| =<sub>''A''</sub>
| <math>=_\text{A}</math>
| "u"
| <math>{}^{\backprime\backprime} \text{u} {}^{\prime\prime}</math>
|}
|}
and the semiotic partition: {{"A", "i"}, {"B", "u"}}.
and the semiotic partition: <math>\{ \{ {}^{\backprime\backprime} \text{A} {}^{\prime\prime}, {}^{\backprime\backprime} \text{i} {}^{\prime\prime} \} , \{ {}^{\backprime\backprime} \text{B} {}^{\prime\prime}, {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \} \}</math>.
In contrast, the SER for interpreter ''B'' yields the semiotic equations:
In contrast, the SER for interpreter <math>\text{B}</math> yields the semiotic equations:
{| cellpadding=4 style="text-align:center"
{| cellpadding="10"
| align=left cellpadding=0 width=10% |
| width="10%" |
| ["A"]<sub>''B''</sub>
| <math>[{}^{\backprime\backprime} \text{A} {}^{\prime\prime}]_\text{B}</math>
| =
| <math>=</math>
| ["u"]<sub>''B''</sub>
| <math>[{}^{\backprime\backprime} \text{u} {}^{\prime\prime}]_\text{B}</math>
| ,
| width="20%" |
| ["B"]<sub>''B''</sub>
| <math>[{}^{\backprime\backprime} \text{B} {}^{\prime\prime}]_\text{B}</math>
| =
| <math>=</math>
| ["i"]<sub>''B''</sub>
| <math>[{}^{\backprime\backprime} \text{i} {}^{\prime\prime}]_\text{B}</math>
|-
|-
| align=left cellpadding=0 width=10% | or
| width="10%" | or
| "A"
| <math>{}^{\backprime\backprime} \text{A} {}^{\prime\prime}</math>
| =<sub>''B''</sub>
| <math>=_\text{B}</math>
| "u"
| <math>{}^{\backprime\backprime} \text{u} {}^{\prime\prime}</math>
| ,
| width="20%" |
| "B"
| <math>{}^{\backprime\backprime} \text{B} {}^{\prime\prime}</math>
| =<sub>''B''</sub>
| <math>=_\text{B}</math>
| "i"
| <math>{}^{\backprime\backprime} \text{i} {}^{\prime\prime}</math>
|}
|}
and the semiotic partition: {{"A", "u"}, {"B", "i"}}.
and the semiotic partition: <math>\{ \{ {}^{\backprime\backprime} \text{A} {}^{\prime\prime}, {}^{\backprime\backprime} \text{u} {}^{\prime\prime} \} , \{ {}^{\backprime\backprime} \text{B} {}^{\prime\prime}, {}^{\backprime\backprime} \text{i} {}^{\prime\prime} \} \}</math>.