数理逻辑

British mathematician, philosopher and Nobel Prize winner Alfred North Whitehead (co-author, with Bertrand Russell , of Principia Mathematica , widely considered by specialists in the subject to be one of the most important and seminal works in mathematical logic and philosophy) declared

英国数学家，哲学家，诺贝尔奖获得者Alred North Whitehead（与Bertrand Russell共同撰写数学基本原理，是一个被专家普遍认为在相关数理逻辑和哲学主题内最重要最学术的作品）宣称

The most important development in mathematical logic for the philosophy of mathematics was Godel's proof that any axiomatic system powerful enough to formalise arithmetic will be incomplete in the sense that there will be truths which are not provable within the system.

数理逻辑中最重要的数学哲学的发展是哥德尔的证明，任何公理系统足够强大以正式算术将在这个意义上不完全会有真理不属于系统内证明的。

Combinatorial theory was adopted to build the general model of predicative concepts , which were further defined on the conjunctive normal form and the disjunctive normal form of prepositional logic Then we set up the concepts evaluation model consisting of the indexes as completeness, consistency, simplicity and inner consistency.

应用数理逻辑理论，定义了基于CNF范式和DNF范式的概念的命题逻辑表示形式，建立了包含概念的完整性、一致性、简单性和内部一致性的比较完整的概念评价的指标体系和模型。

Unifying themes in mathematical logic include the expressive power of formal logics and the deductive power of formal proof systems.

数理逻辑和电脑科学有许多重合之处，这是因为许多电脑科学的先驱者既是数学家、又是逻辑学家，如阿兰·图灵，邱奇等。

On one side, he inherits the tradition of pragmatism, on the other side , he emphasizes the effect to philosophy from logic and mathematics. His emphasis on mathematical logic, meaning theory and experience verify theory, which makes up pragmatic insufficience.

在刘易斯那里，他一方面继承实用主义的传统，另一方面又强调逻辑和数学对哲学的影响，重视对数理逻辑的研究，重视对意义理论、经验证实理论等等的探讨，弥补了实用主义在这方面的不足。

As von Neumann computers are based on the theory of mathematical logic, current computers are incomparably successful in processing mathematical problems. However, it's very difficult for them to process linguistical information such as natural language.

由于冯。诺依曼式计算机的理论基础是数理逻辑，现今的计算机处理数理问题无比成功，然而处理自然语言等文理信息却非常困难。

There had been three climaxes in investigating paradox in the logical history of the west. Especially the appearance of Rusells paradox leads to the third climax of the research into the paradox, which has directly accelerated the formation and development of mathematical logic.

在西方逻辑史上，曾有过三次悖论研究的高潮，尤其是罗素悖论所引发的第三次高潮，直接促进了数理逻辑的形成和发展。

But it is not a whole failure. Russell' contribution lies in his study of mathematics logicism promoting the development of mathematics logic.

但这种失败只是部分失败，其成功之处在于，罗素的数学逻辑主义研究对数理逻辑的发展作出了重要的贡献。

Traditional logic' s answer to this question seems to be self-evident, but mathematical logic makes this question complicated.

传统逻辑对这个问题的回答似乎是不言而喻的，但数理逻辑却使这个问题变得复杂起来。

This book is a rigorous elementary introduction to classical predicate logic emphasizing that deduction is a form of computation.

这是一本结合逻辑在计算机科学中的应用来介绍数理逻辑的教科书，书中强调了演绎作为计算的一种形式的概念。

Do not gum up the work by telling mother what we are going to do .

别告诉母亲我们要干的事，那会把事情搞糟的。

In recent years, application of the partial prestressed concrete beam s is developed.

近年来，随着部分预应力砼梁应用的推广，发现我国规范所采用的名义拉应力法的计算结果不稳定。