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sav08:simple_qe_for_dense_linear_orders [2009/04/21 23:59] vkuncak |
sav08:simple_qe_for_dense_linear_orders [2009/04/22 12:08] vkuncak |
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| Formulas $T$ are the formulas that are closed formulas that are true in the structure $(\mathbb{Q},<)$ or rational numbers. | Formulas $T$ are the formulas that are closed formulas that are true in the structure $(\mathbb{Q},<)$ or rational numbers. | ||
| - | **Example:** | + | **Example:** The 'successor' formula: |
| \[ | \[ | ||
| \forall x. \exists y.\ x < y \ \land\ (\forall z. (x < z \rightarrow z=y \lor y < z) | \forall x. \exists y.\ x < y \ \land\ (\forall z. (x < z \rightarrow z=y \lor y < z) | ||
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| Quantifier elimination from more general formulas: | Quantifier elimination from more general formulas: | ||
| - | * [[http://www4.informatik.tu-muenchen.de/~nipkow/pubs/lqe.pdf|Linear Quantifier Elimination]] | + | **Example:** Use quantifier elimination to compute the truth value in dense linear orders for the example 'successor' formula above. |
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| + | ===== References ===== | ||
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| + | * [[http://www4.informatik.tu-muenchen.de/~nipkow/pubs/lqe.pdf|Linear Quantifier Elimination]] (Tobias Nipkow, IJCAR 2008) | ||
| * [[http://citeseer.ist.psu.edu/loos93applying.html|Applying Linear Quantifier Elimination]] | * [[http://citeseer.ist.psu.edu/loos93applying.html|Applying Linear Quantifier Elimination]] | ||
| * [[http://citeseer.ist.psu.edu/71579.html|Parallel Fourier-Motzkin Elimination]] | * [[http://citeseer.ist.psu.edu/71579.html|Parallel Fourier-Motzkin Elimination]] | ||