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sav08:semidecision_procedure_for_first-order_logic_without_equality [2008/03/20 12:21] vkuncak created |
sav08:semidecision_procedure_for_first-order_logic_without_equality [2009/05/14 13:19] vkuncak |
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| ====== Semidecision Procedure for Validity of Formulas in First-Order Logic ====== | ====== Semidecision Procedure for Validity of Formulas in First-Order Logic ====== | ||
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| + | [[wp>Davis–Putnam algorithm]] | ||
| Suppose $S$ has no model. | Suppose $S$ has no model. | ||
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| Then $propExpand(S)$ has no model. | Then $propExpand(S)$ has no model. | ||
| - | By compactness, some finite subset has no model. | + | By propositional [[Compactness Theorem]], some finite subset has no model. |
| Can check satisfiability of larger and larger initial prefixes of $propExpand(S)$ using a SAT solver. | Can check satisfiability of larger and larger initial prefixes of $propExpand(S)$ using a SAT solver. | ||