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sav08:idea_of_quantifier-free_combination [2008/04/24 13:50] vkuncak |
sav08:idea_of_quantifier-free_combination [2015/04/21 17:30] |
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| - | ====== Idea of Quantifier-Free Combination ====== | ||
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| - | We wish to reason about quantifier-free formulas that contain different symbols, such as | ||
| - | * ground formulas interpreted over arbitrary functions and relations (also called uninterpreted function symbols) | ||
| - | * term algebras (interpreted over Herbrand model) | ||
| - | * integer linear arithmetic | ||
| - | * real linear arithmetic | ||
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| - | For this, we would like to separate a quantifier-free formula into constraints that talk only about individual theories, and solve each constraint separately. | ||
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| - | Note that we are checking satisfiability, and $F$ is satisfiable iff each disjunct in its disjunctive normal form is satisfiable. We therefore consider conjunctions of literals. | ||
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| - | Consider a conjunction of literlas $C$. If we can represent it as separate conjunction $C_1$,...,$C_n$ then | ||
| - | * if one of the $C_i$ is unsatisfiable, then $C$ is unsatisfiable | ||
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| - | The idea is to separate conjuncts into those specific to individual theories, and then solve each $C_i$ using a specialized decision procedure $P_i$ | ||
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| - | An important question is completeness: if each $C_i$ is satisfiable, is $C_1 \land \ldots \land C_n$ satisfiable? We will show that, under certain conditions, this holds. | ||