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arXiv 1701.00629cs.PLcs.LO
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无限域上的约束逻辑规划及其在证明中的应用

Constraint Logic Programming over Infinite Domains with an Application to Proof

Sebastian Krings, Michael Leuschel

摘要:

我们提出了一个基于CLP(FD)的约束求解器,能够处理无界域。它基于约束传播,如果所有其他方法都失败,则诉诸枚举。一个重要的方面是检测枚举何时完成,以及这是否对结果的可靠性有影响。我们提出了一种技术,保证健全的方式如下:如果约束求解器找到一个解决方案,它保证是正确的;如果约束求解器未能找到一个解决方案,它可以返回的结果“绝对假”的情况下,它知道枚举是详尽的,或“未知”的情况下,它被中止。该技术可以处理嵌套的全称量词和存在量词。它可以很容易地扩展到集合解析和其他引入新量化变量的运算符。我们展示了数据验证和证明中的应用。

英文摘要:

We present a CLP(FD)-based constraint solver able to deal with unbounded domains. It is based on constraint propagation, resorting to enumeration if all other methods fail. An important aspect is detecting when enumeration was complete and if this has an impact on the soundness of the result. We present a technique which guarantees soundness in the following way: if the constraint solver finds a solution it is guaranteed to be correct; if the constraint solver fails to find a solution it can either return the result "definitely false" in case it knows enumeration was exhaustive, or "unknown" in case it was aborted. The technique can deal with nested universal and existential quantifiers. It can easily be extended to set comprehensions and other operators introducing new quantified variables. We show applications in data validation and proof.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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