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sav08:definition_of_set_constraints [2008/05/22 11:51] vkuncak |
sav08:definition_of_set_constraints [2008/05/22 11:51] vkuncak |
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- | An important property we would like to have in this semantic is a very intuitive one : \[ [[f^{-1}(f(S_1, S_2))]] = [[S_1]] \] | ||
- | This property is in fact not conserved as we can easily see using a very simple counter-example : | ||
- | \[ [[f^{-1}(f(S_1, \emptyset))]] = [[f^{-1}(\lbrace f(t_1, t_2) | t_1 \in [[S_1]] \wedge t_2 \in \emptyset \rbrace)]] = [[f^{-1}(\emptyset)]] = \emptyset \] | ||
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- | The correct interpretation of this property is : | ||
- | \begin{displaymath} [[f^{-1}(f(S_1, S_2))]] = \left\{ \begin{array}{ll} | ||
- | \emptyset & if [[S_2]] = \emptyset & | ||
- | [[S_1]] & otherwise \\ | ||
- | \end{array} \right \end{displaymath} | ||
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