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, 17:30, 28 April 2008
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| The proposition or the truth-function <math>q\!</math> that describes <math>Q\!</math>is: | | The proposition or the truth-function <math>q\!</math> that describes <math>Q\!</math>is: |
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− | : <code>(( u v )( u w )( v w ))</code> | + | : <code> (( u v )( u w )( v w )) </code> |
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| Conjoining the query that specifies the center cell gives: | | Conjoining the query that specifies the center cell gives: |
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− | : <code>(( u v )( u w )( v w )) u v w</code> | + | : <code> (( u v )( u w )( v w )) u v w </code> |
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| And we know the value of the interpretation by whether this last expression issues in a model. | | And we know the value of the interpretation by whether this last expression issues in a model. |
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| </code> | | </code> |
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− | <pre>
| + | The models of this last expression tell us which combinations of feature changes among the set <math>\{ \operatorname{d}u, \operatorname{d}v, \operatorname{d}w \}</math> will take us from our present interpretation, the center cell expressed by "<math>u\ v\ w</math>", to a true value under the target proposition <code> (( u v )( u w )( v w )) </code>. |
− | The models of this last expression tell us which combinations of | |
− | feature changes among the set {du, dv, dw} will take us from our | |
− | present interpretation, the center cell expressed by "u v w", to | |
− | a true value under the target proposition (( u v )( u w )( v w )). | |
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− | The result of applying the difference operator D | + | The result of applying the difference operator <math>\operatorname{D}</math> to the initial proposition <math>\operatorname{q}</math>, conjoined with a query on the center cell, yields: |
− | to the initial proposition q, conjoined with | |
− | a query on the center cell, yields: | |
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| + | <code> |
| ( | | ( |
| (( ( u , du )( v , dv ) | | (( ( u , du )( v , dv ) |
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| )) | | )) |
| ) | | ) |
− | | + | |
| u v w | | u v w |
| + | </code> |
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| The models of this last proposition are: | | The models of this last proposition are: |
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| + | <code> |
| 1. u v w du dv dw | | 1. u v w du dv dw |
| 2. u v w du dv (dw) | | 2. u v w du dv (dw) |
| 3. u v w du (dv) dw | | 3. u v w du (dv) dw |
| 4. u v w (du) dv dw | | 4. u v w (du) dv dw |
| + | </code> |
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− | This tells us that changing any two or more of the | + | This tells us that changing any two or more of the features <math>u, v, w</math> will take us from the center cell to a cell outside the shaded region for the set <math>Q\!</math>. |
− | features u, v, w will take us from the center cell | |
− | to a cell outside the shaded region for the set Q. | |
− | </pre> | |
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| ===Note 4=== | | ===Note 4=== |