| Title: | 程序正确性逻辑验证的一些探讨 |
| Author: | 薛涛
|
| Issued Date: | 2008-05-29
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| Degree Grantor: | 中国科学院软件研究所
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| Place of Degree Grantor: | 软件研究所
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| Degree Level: | 博士
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| Keyword: | 极小一阶逻辑
; 搜索算法
; Kripke模型
|
| Alternative Title: | A study on logic method for programme correctness verification
|
| 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。 |
| English 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. |
| Language: | 中文
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| Content Type: | 学位论文
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| URI: | http://ir.iscas.ac.cn/handle/311060/7254
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| Appears in Collections: | 中科院软件所
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| File Name/ File Size |
Content Type |
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| 10001_200528015029006薛涛_paper.pdf（515KB） | -- | -- | 限制开放 | -- | 联系获取全文 |
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| Recommended Citation: | |
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. 2008-05-29.
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