undecidability

简明释义

英[ˌʌndɪˌsaɪdəˈbɪlɪti]美[ˈʌndɪsaɪdəˈbɪləti]

n. [数] 不可判定性

英英释义

单词用法

同义词

反义词

例句

1.That's the negative response to undecidability, and it's of course, a view that many of us may entertain.

那就是对不可判定性的一个消极的反应，当然，我们可以容纳这个观点。

2.That's the negative response to undecidability, and it's of course, a view that many of us may entertain.

那就是对不可判定性的一个消极的反应，当然，我们可以容纳这个观点。

3.Philosophers often debate the undecidability 不可判定性 of certain ethical dilemmas.

哲学家们常常讨论某些伦理困境的 undecidability 不可判定性 。

4.The undecidability 不可判定性 of the truth of some propositions means we can't always prove or disprove them.

某些命题的 undecidability 不可判定性 意味着我们并不总能证明或反驳它们。

5.In formal logic, the undecidability 不可判定性 of certain statements poses challenges for mathematicians.

在形式逻辑中，某些陈述的 undecidability 不可判定性 给数学家带来了挑战。

6.The famous Halting Problem is a classic example of undecidability 不可判定性 in algorithms.

著名的停机问题是算法中 undecidability 不可判定性 的经典例子。

7.In computer science, the concept of undecidability 不可判定性 is crucial for understanding the limits of what can be computed.

在计算机科学中，undecidability 不可判定性 的概念对于理解计算的限制至关重要。

作文

In the field of mathematics and computer science, the concept of undecidability plays a crucial role in understanding the limits of computation and formal systems. Undecidability refers to the property of certain problems that cannot be resolved by any algorithm or mechanical process. This notion was famously illustrated by Alan Turing in the 1930s through his work on the Halting Problem, which demonstrated that there is no general algorithm capable of determining whether a given program will finish running or continue indefinitely. This revelation not only reshaped the landscape of theoretical computer science but also raised profound philosophical questions about the nature of computation and the limits of human knowledge.To grasp the implications of undecidability, one must first understand what it means for a problem to be decidable. A problem is considered decidable if there exists an algorithm that can provide a correct yes-or-no answer for every input in a finite amount of time. For instance, determining whether a number is prime is a decidable problem because there are algorithms that can efficiently resolve it. In contrast, problems characterized by undecidability lack such algorithms, leaving them perpetually unresolved.The significance of undecidability extends beyond theoretical discussions; it has practical implications in various domains, including software development, artificial intelligence, and even legal systems. For instance, in software engineering, certain properties of programs, such as their correctness, may be undecidable. This means that developers cannot create a tool that guarantees the detection of all potential errors in their code, leading to challenges in ensuring software reliability. Similarly, in artificial intelligence, some decision-making problems exhibit undecidability, complicating the development of AI systems that require definitive answers.Philosophically, undecidability raises intriguing questions about the nature of truth and knowledge. If certain truths are inherently undecidable, what does that imply about our ability to understand the universe? This question resonates with the works of mathematicians like Kurt Gödel, who proved that in any sufficiently powerful axiomatic system, there exist true statements that cannot be proven within that system. Gödel's incompleteness theorems highlight the limitations of formal systems and echo the theme of undecidability in computation.Furthermore, the concept of undecidability can be applied to real-world scenarios, such as ethical dilemmas or complex societal issues. When faced with a moral decision, individuals often encounter situations where no clear right or wrong answer exists. These scenarios can be likened to undecidable problems in that they challenge our capacity to arrive at a definitive conclusion. Such parallels illustrate how undecidability permeates not only the realms of mathematics and computer science but also the fabric of human experience.In conclusion, undecidability is a profound concept that transcends the boundaries of mathematics and computer science, influencing philosophical thought and practical applications alike. By recognizing the existence of undecidability, we gain insight into the limitations of our computational tools and the complexities of the problems we face. Embracing this notion invites us to explore the unknown and acknowledge that some questions may remain forever unanswered, challenging our understanding of knowledge and truth.

在数学和计算机科学领域，undecidability（不可判定性）这一概念在理解计算和形式系统的局限性方面发挥着至关重要的作用。Undecidability指的是某些问题的特性，这些问题无法通过任何算法或机械过程得到解决。这个概念在20世纪30年代由艾伦·图灵通过对停机问题的研究而著名地阐明，停机问题表明不存在一种通用算法可以确定给定程序是否会停止运行或无限期继续。这一发现不仅重塑了理论计算机科学的格局，还引发了关于计算本质和人类知识局限性的深刻哲学问题。要理解undecidability的含义，首先必须了解问题可判定的含义。如果存在一个算法能够为每个输入在有限时间内提供正确的“是”或“否”的答案，则该问题被认为是可判定的。例如，判断一个数字是否为素数就是一个可判定的问题，因为存在能够有效解决它的算法。相反，具有undecidability特征的问题缺乏这样的算法，导致它们永远无法解决。Undecidability的重要性不仅限于理论讨论；它在软件开发、人工智能甚至法律系统等多个领域都有实际影响。例如，在软件工程中，程序的某些属性，如其正确性，可能是undecidable（不可判定的）。这意味着开发人员无法创建一个工具来保证检测到代码中的所有潜在错误，从而在确保软件可靠性方面面临挑战。同样，在人工智能领域，一些决策问题表现出undecidability，使得开发需要明确答案的AI系统变得复杂。从哲学的角度来看，undecidability引发了关于真理和知识本质的有趣问题。如果某些真理本质上是undecidable的，那么这对我们理解宇宙的能力意味着什么？这个问题与数学家库尔特·哥德尔的工作产生了共鸣，他证明在任何足够强大的公理系统中，存在一些在该系统内无法证明的真命题。哥德尔的不完全性定理突显了形式系统的局限性，并呼应了计算中的undecidability主题。此外，undecidability的概念可以应用于现实世界的场景，例如伦理困境或复杂的社会问题。当面对道德决策时，个人经常会遇到没有明确对错答案的情况。这些情境可以比作undecidable问题，因为它们挑战着我们得出明确结论的能力。这种类比说明了undecidability不仅渗透于数学和计算机科学的领域，也深入人类经验的本质。总之，undecidability是一个深刻的概念，它超越了数学和计算机科学的界限，对哲学思考和实际应用产生了影响。通过认识到undecidability的存在，我们可以洞察到我们计算工具的局限性以及我们面临问题的复杂性。接受这一概念邀请我们探索未知，并承认某些问题可能永远没有答案，这挑战了我们对知识和真理的理解。