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, 16:58, 5 May 2008
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| Applying the enlargement operator <math>\operatorname{E}</math> to the initial proposition <math>q\!</math> yields: | | Applying the enlargement operator <math>\operatorname{E}</math> to the initial proposition <math>q\!</math> yields: |
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− | <code> | + | <pre> |
| (( ( u , du )( v , dv ) | | (( ( u , du )( v , dv ) |
| )( ( u , du )( w , dw ) | | )( ( u , du )( w , dw ) |
| )( ( v , dv )( w , dw ) | | )( ( v , dv )( w , dw ) |
| )) | | )) |
− | </code> | + | </pre> |
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| Conjoining a query on the center cell yields: | | Conjoining a query on the center cell yields: |
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− | <code> | + | <pre> |
| (( ( u , du )( v , dv ) | | (( ( u , du )( v , dv ) |
| )( ( u , du )( w , dw ) | | )( ( u , du )( w , dw ) |
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| u v w | | u v w |
− | </code> | + | </pre> |
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| 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 <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>. |
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| 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: | | 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: |
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− | <code> | + | <pre> |
| ( | | ( |
| (( ( u , du )( v , dv ) | | (( ( u , du )( v , dv ) |
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| u v w | | u v w |
− | </code> | + | </pre> |
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| The models of this last proposition are: | | The models of this last proposition are: |
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− | <code> | + | <pre> |
| 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> | + | </pre> |
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− | 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>. | + | 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> |
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| ===Note 4=== | | ===Note 4=== |