axiomatization

简明释义

英[ˌæksiəmətaɪˈzeɪʃən]美[ˌæksiəmətaɪˈzeɪʃən]

n. 公理化（用公理方法研究数学以及其他学科）

英英释义

单词用法

同义词

反义词

例句

1.Based on the axiomatization definitions of subsethood measure and similarity measure, similarity measuer induced by subsethood measure is discussed, and some real induced formulas are given.

依据包含度和贴近度的公理化定义，讨论了由包含度诱导的贴近度，给出了一些具体的诱导公式。

2.Based on the axiomatization definitions of subsethood measure and similarity measure, similarity measuer induced by subsethood measure is discussed, and some real induced formulas are given.

依据包含度和贴近度的公理化定义，讨论了由包含度诱导的贴近度，给出了一些具体的诱导公式。

3.These achievements include the axiomatization of programming languages and data types, formal verification, and formal specification and analysis.

这些贡献包括编程语言和数据类型的公理化，形式验证，形式规约与分析。

4.Therefore no formal system is a true axiomatization of full number theory.

因此，没有正式的系统是一个真正的公理化充分一些理论。

5.Axiomatization of economic theory has many obvious advantage.

经济理论的公理化有很多明显的优越性。

6.The mathematician proposed an axiomatization 公理化 of geometry that simplified many complex theories.

这位数学家提出了一种简化许多复杂理论的几何公理化。

7.In computer science, the axiomatization 公理化 of algorithms helps in proving their correctness.

在计算机科学中，算法的公理化有助于证明它们的正确性。

8.The axiomatization 公理化 of set theory laid the groundwork for modern mathematics.

集合论的公理化为现代数学奠定了基础。

9.Philosophers often debate the axiomatization 公理化 of ethical principles.

哲学家们常常讨论伦理原则的公理化。

10.His research focused on the axiomatization 公理化 of logical systems.

他的研究集中在逻辑系统的公理化上。

作文

In the realm of mathematics and logic, one of the most significant processes is the axiomatization. This term refers to the method of establishing a set of axioms or foundational principles from which other truths can be derived. The importance of axiomatization cannot be overstated, as it is the bedrock upon which entire fields of study are built. Axioms are statements that are accepted as true without proof, serving as the starting point for further reasoning and argumentation. For instance, in Euclidean geometry, the five postulates laid out by Euclid serve as the axiomatic foundation from which all other geometric truths follow. To illustrate the power of axiomatization, consider the development of calculus. Isaac Newton and Gottfried Wilhelm Leibniz independently formulated the principles of calculus, but it was not until later that mathematicians sought to formalize these concepts through axiomatic systems. The axiomatization of calculus allowed for a clearer understanding of limits, derivatives, and integrals, providing a robust framework for mathematical analysis. Moreover, axiomatization extends beyond mathematics into various disciplines such as physics, computer science, and even philosophy. In physics, for example, the laws of motion formulated by Sir Isaac Newton can be seen as an axiomatization of classical mechanics. These laws serve as fundamental truths from which predictions about the physical world can be made. Similarly, in computer science, the axiomatization of algorithms allows for systematic problem-solving approaches that are essential for programming and software development. The process of axiomatization also plays a crucial role in the philosophy of mathematics. Philosophers like David Hilbert advocated for a rigorous axiomatization of mathematics to ensure its consistency and completeness. Hilbert's program aimed to show that all mathematical truths could be derived from a finite set of axioms, thereby reinforcing the reliability of mathematical knowledge. However, Gödel's incompleteness theorems later revealed limitations in this approach, showing that not all mathematical truths can be captured through axiomatization alone. Additionally, axiomatization encourages critical thinking and logical reasoning. By establishing clear axioms, individuals are prompted to analyze and question the validity of their assumptions. This process fosters a deeper understanding of the subject matter and promotes intellectual rigor. In academic writing, for instance, the clear axiomatization of arguments aids in constructing persuasive essays and research papers, as it allows authors to build their cases on solid foundations. In conclusion, axiomatization is a fundamental concept that permeates various fields of study. It provides a structured approach to understanding complex ideas by breaking them down into simpler, more manageable components. Whether in mathematics, physics, computer science, or philosophy, the significance of axiomatization lies in its ability to establish a coherent framework for reasoning and exploration. As we continue to advance our knowledge across disciplines, the principles of axiomatization will remain essential in guiding our inquiries and shaping our understanding of the world around us.

在数学和逻辑领域，最重要的过程之一是公理化。这个术语指的是建立一组公理或基础原则的方法，从中可以推导出其他真理。公理化的重要性不容小觑，因为它是整个研究领域的基石。公理是被接受为真实而无需证明的陈述，作为进一步推理和论证的起点。例如，在欧几里得几何中，欧几里得列出的五个公设作为所有其他几何真理的公理基础。 为了说明公理化的力量，考虑微积分的发展。艾萨克·牛顿和戈特弗里德·威廉·莱布尼茨独立地提出了微积分的原则，但直到后来，数学家们才寻求通过公理系统来形式化这些概念。微积分的公理化使得对极限、导数和积分的理解更加清晰，为数学分析提供了一个坚实的框架。 此外，公理化不仅存在于数学领域，还扩展到物理学、计算机科学，甚至哲学等多个学科。在物理学中，例如，艾萨克·牛顿制定的运动定律可以看作是经典力学的公理化。这些定律作为基本真理，从中可以对物理世界做出预测。同样，在计算机科学中，算法的公理化允许系统化的问题解决方法，这对编程和软件开发至关重要。 公理化的过程在数学哲学中也发挥着至关重要的作用。大卫·希尔伯特等哲学家倡导对数学进行严格的公理化以确保其一致性和完整性。希尔伯特计划旨在证明所有数学真理都可以从有限的一组公理中推导出来，从而增强数学知识的可靠性。然而，哥德尔的不完备性定理后来揭示了这种方法的局限性，表明并非所有数学真理都可以仅通过公理化来捕捉。 此外，公理化鼓励批判性思维和逻辑推理。通过建立明确的公理，个人被促使分析和质疑他们假设的有效性。这个过程促使对主题的更深刻理解，并促进智力的严谨性。在学术写作中，例如，清晰的公理化论点有助于构建有说服力的论文和研究报告，因为它允许作者在坚实的基础上建立他们的论据。 总之，公理化是一个贯穿各个学科的基本概念。它通过将复杂的思想分解成更简单、更易管理的组成部分，提供了一种结构化的方法来理解这些思想。无论是在数学、物理学、计算机科学还是哲学领域，公理化的重要性在于它能够建立一个连贯的推理和探索框架。随着我们在各个学科知识的不断进步，公理化的原则将继续在引导我们的探究和塑造我们对周围世界的理解中发挥重要作用。