Formalization of linear space theory in the higher-order logic proving system

Zhang J.; Mao D.; Guan Y.

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Formalization of linear space theory in the higher-order logic proving system

机译：高阶逻辑证明系统中线性空间理论的形式化

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Theorem proving is an important approach in formal verification. Higher-order logic is a form of predicate logic that is distinguished from first-order logic by additional quantifiers and stronger semantics. Higher-order logic is more expressive. This paper presents the formalization of the linear space theory in HOL4. A set of properties is characterized in HOL4. This result is used to build the underpinnings for the application of higher-order logic in a wider spectrum of engineering applications.

机译：定理证明是形式验证的重要方法。高阶逻辑是谓词逻辑的一种形式，通过附加的量词和更强的语义与一阶逻辑区分开。高阶逻辑更具表现力。本文介绍了HOL4中线性空间理论的形式化。一组属性在HOL4中进行了表征。该结果用于为更广泛的工程应用中的高阶逻辑应用奠定基础。

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《Journal of applied mathematics》 |2013年第2期|共6页
作者
Zhang J.; Mao D.; Guan Y.;
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正文语种 eng
中图分类 51.9;
关键词
Formalization of linear space; theory in the higher-order logic; proving system;

机译：线性空间的形式化;高阶逻辑理论;证明系统;

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专利

1. Formalization of linear space theory in the higher-order logic proving system [J] . Zhang J., Mao D., Guan Y. Journal of applied mathematics . 2013,第Pta2期

机译：高阶逻辑证明系统中线性空间理论的形式化
2. Formalization of Metatheory of the Quipper Quantum Programming Language in a Linear Logic [J] . Mahmoud Mohamed Yousri, Felty Amy P. Journal of Automated Reasoning . 2019,第4期

机译：线性逻辑中Quipper量子编程语言的Metathory的形式化
3. Formalized meta-theory of sequent calculi for linear logics [J] . Chaudhuri Kaustuv, Lima Leonardo, Reis Giselle Theoretical computer science . 2019,第期

机译：用于线性逻辑的形式化元化学元理论
4. FORMALIZATION OF FRACTIONAL FLOW COMPONENT IN HIGHER-ORDER LOGIC THEOREM PROVING [C] . Chunna Zhao, Murong Jiang, Yaqun Huang International Design Engineering Technical Conferences;Computers and Information in Engineering Conference;IEEE/ASME International Conference on Mechatronic and Embedded Systems and Applications . 2019

机译：高阶逻辑定理证明中的分式流分量的形式化
5. APPLICATIONS OF TOPOLOGICAL VECTOR SPACES TO LINEAR SYSTEM THEORY. [D] . HEGNER, STEPHEN JAMES. 1977

机译：拓扑向量空间在线性系统理论中的应用。
6. ON THE UNIFICATION OF THE CALCULUS OF VARIATIONS AND THE THEORY OF MONOTONE NONLINEAR OPERATORS IN BANACH SPACES [O] . Felix E. Browder 1966

机译：Banach空间中变量的计算统一和单调非线性算子理论。
7. Foundational, compositional (co)datatypes for higher-order logic: category theory applied to theorem proving [O] . Traytel, Dmitriy, Popescu, Andrei, Blanchette, Jasmin 2012

机译：高阶逻辑的基础，组合（共）数据类型：类别理论应用于定理证明
8. Automated Theorem Proving in the Theory of Approximate Reasoning, with Applications to Logic Programming and Expert Systems. [R] . Schwartz, D. G. 1991

机译：近似推理理论中的自动定理证明及其在逻辑程序设计和专家系统中的应用。

Formalization of linear space theory in the higher-order logic proving system

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