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sav08:definition_of_set_constraints [2008/05/22 11:51] vkuncak |
sav08:definition_of_set_constraints [2008/05/22 11:55] vkuncak |
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| Line 109: | Line 109: | ||
| Let us simplify this expression: | Let us simplify this expression: | ||
| \[ | \[ | ||
| - | f^{-2}(f(S,T)) = | + | f^{-1}(f(S,T)) = |
| \] | \] | ||
| ++| | ++| | ||
| \[ | \[ | ||
| - | = f^{-2}(\{ f(s,t) \mid s \in S, t \in T \}) | + | = f^{-1}(\{ f(s,t) \mid s \in S, t \in T \}) |
| \] | \] | ||
| ++ | ++ | ||
| Line 130: | Line 130: | ||
| \] | \] | ||
| ++ | ++ | ||
| + | |||
| + | Consider conditional constraints of the form | ||
| + | \[ | ||
| + | T \neq \emptyset \rightarrow S_1 \subseteq S_2 | ||
| + | \] | ||
| + | We can transform it into | ||
| + | \[ | ||
| + | f(S_1,T) \subseteq f(S_2,T) | ||
| + | \] | ||
| + | for some binary function symbol $f$. Thus, we can introduce such conditional constraints without changing expressive power or decidability. | ||