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| 程序正确性逻辑验证的一些探讨 | |
| Alternative Title | A study on logic method for programme correctness verification |
| 薛涛 | |
| 2008-05-29 | |
| Degree Grantor | 中国科学院软件研究所 |
| Degree Level | 博士 |
| Place of Degree Grantor | 软件研究所 |
| Keyword | 极小一阶逻辑 搜索算法 Kripke模型 |
| English Abstract | 搜索算法是逻辑证明中的经典方法，广泛用于直觉主义逻辑，古典逻辑等多种逻辑系统。Kripke模型是一个非常简单而有效的模型，它能对解释直觉主义逻辑的语义给予合理的解释。 本文的主要工作是给出了一个极小一阶逻辑下闭的正公式的搜索算法。该算法基于极小一阶逻辑下闭的正公式证明的可判定性，在[13]的LJB系统中的搜索算法基础上，将[21] 在简单类型理论中的反例构造算法进行拓展，对于任意极小一阶逻辑下闭的正公式，可证的给出证明，不可证的构造一个Kripke模型的反例。随后我们对该算法的正确性以及相关性质给出了证明。 |
| Abstract | Proof search is a classical method in logic proof. It is widely used in many logic systems, for example, intuitionistic logic and classical logic. Kripke model is a fairly simple and convenient model for the semantics of intuitionistic logic. The main work of this paper is that we present an algorithm of proof search for positive formulas in minimal predicate logic. It is based on the LJB deduction system introduced in [13], and extended the counter model constructing algorithm in simple typed theory in [21] . The algorithm returns a deduction tree, and hence a proof, when the formula is provable, and a Kripke model will be constructed as a counter-model when the formula is unprovable. The soundness and the completeness are proved. |
| Pages | 66 |
| Language | 中文 |
| Content Type | 学位论文 |
| URI | http://ir.iscas.ac.cn/handle/311060/7254 |
| Collection | 中科院软件所_中科院软件所 |
| Recommended Citation GB/T 7714 | 薛涛. 程序正确性逻辑验证的一些探讨[D]. 软件研究所. 中国科学院软件研究所,2008. |
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| File Name/Size | DocType | Version | Access | License | ||
| 10001_20052801502900（515KB） | 限制开放 | -- | Application Full Text | |||
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