provability

简明释义

英[prəˈvuːəˌbɪlɪti]美[prəˈvuːəˌbɪlɪti]

n. 可证明

英英释义

单词用法

同义词

反义词

例句

1.The responsible degree of damages should be limited by the provability of medical inspection. In the considerations of illegality and harmful facts, the environmental standards were not concerned.

污染损害可归责的程度应以医学观察的可证明性为界限，在违法性和损害事实考量中，环境标准均非所问。

2.The responsible degree of damages should be limited by the provability of medical inspection. In the considerations of illegality and harmful facts, the environmental standards were not concerned.

污染损害可归责的程度应以医学观察的可证明性为界限，在违法性和损害事实考量中，环境标准均非所问。

3.So, for the price of at most a few instructions, your program can have the provability of a functional program and the speed and memory characteristics of an imperative one.

从而，在只是付出了一些指令的代价后，您的程序会拥有函数式程序的可证明性和命令式程序的速度和内存特性。

4.In legal contexts, the provability of evidence is essential for securing convictions.

在法律背景下，证据的可证明性对于确保定罪至关重要。

5.The provability of certain statements in logic can lead to significant philosophical discussions.

逻辑中某些陈述的可证明性可能引发重要的哲学讨论。

6.In mathematics, the concept of provability is crucial for establishing the validity of theorems.

在数学中，可证明性的概念对于建立定理的有效性至关重要。

7.The provability of a hypothesis often requires extensive experimentation and data analysis.

一个假设的可证明性通常需要广泛的实验和数据分析。

8.Researchers are investigating the provability of complex algorithms in computer science.

研究人员正在调查计算机科学中复杂算法的可证明性。

作文

In the realm of mathematics and logic, the concept of provability plays a crucial role in determining the validity of statements and theorems. Provability refers to the ability to demonstrate that a certain proposition is true through a series of logical deductions based on established axioms and previously proven theorems. This concept is not only fundamental to mathematics but also extends its influence into computer science, philosophy, and even legal reasoning.To understand the importance of provability, we can look at Gödel's incompleteness theorems, which reveal inherent limitations in formal systems. Gödel showed that there are true mathematical statements that cannot be proven within a given system, highlighting that provability is not an absolute measure of truth. This revelation has profound implications, suggesting that our understanding of mathematical truths is always incomplete and that there are boundaries to what can be formally verified.In practical applications, the concept of provability is essential in fields such as computer science, where algorithms are often designed to check the provability of certain conditions or statements. For example, in programming, when developers write code, they must ensure that their algorithms can produce correct outputs for all possible inputs. This requirement ties back to the idea of provability in that the correctness of an algorithm must be demonstrable through rigorous testing and formal verification methods.Moreover, the notion of provability extends into artificial intelligence, where proving the correctness of AI systems is critical. As AI technologies become more integrated into society, ensuring that these systems operate according to their specifications becomes paramount. The provability of an AI system’s decisions can significantly affect trust and safety in applications ranging from autonomous vehicles to medical diagnostics.In philosophy, provability raises questions about the nature of knowledge and belief. Philosophers have long debated whether something can be considered true if it cannot be proven. This inquiry leads to discussions about skepticism and the foundations of knowledge itself. If we accept that some truths are unprovable, we must grapple with the implications for our understanding of reality and how we justify our beliefs.Legal reasoning also incorporates the concept of provability. In a court of law, the burden of proof lies with the party making a claim. Legal standards often require that evidence be presented in such a way that it can be deemed provable beyond a reasonable doubt. This aspect of provability is vital in ensuring that justice is served and that verdicts are based on solid evidence rather than conjecture.In conclusion, provability is a multifaceted concept that transcends disciplines and influences various fields of study. Whether in mathematics, computer science, philosophy, or law, understanding the limits and implications of provability is essential for advancing knowledge and ensuring the integrity of systems and beliefs. As we continue to explore the frontiers of knowledge, the quest for provability will remain a central theme, challenging us to think critically about what we can know and how we can demonstrate it.

在数学和逻辑领域，provability（可证明性）这一概念在确定陈述和定理的有效性方面发挥着至关重要的作用。Provability指的是通过一系列基于已建立公理和先前证明的定理的逻辑推导来证明某个命题为真的能力。这个概念不仅对数学至关重要，还扩展到计算机科学、哲学甚至法律推理等领域。为了理解provability的重要性，我们可以看看哥德尔的不完备性定理，它揭示了形式系统固有的局限性。哥德尔展示了存在一些在给定系统内无法证明的真实数学陈述，这突显了provability并不是一个绝对的真理衡量标准。这一发现具有深远的影响，表明我们对数学真理的理解总是不完整的，并且存在可以被正式验证的界限。在实际应用中，provability的概念在计算机科学等领域至关重要，因为算法通常被设计用来检查某些条件或陈述的provability。例如，在编程中，当开发者编写代码时，他们必须确保他们的算法能够为所有可能的输入产生正确的输出。这一要求与provability的概念密切相关，因为算法的正确性必须通过严格的测试和形式验证方法来证明。此外，provability的概念延伸到人工智能领域，在这里，证明AI系统的正确性至关重要。随着AI技术越来越多地融入社会，确保这些系统按照其规范操作变得至关重要。AI系统决策的provability可以显著影响从自动驾驶汽车到医学诊断等应用中的信任和安全。在哲学中，provability引发了关于知识和信念本质的问题。哲学家们长期以来一直在辩论，如果某件事情无法被证明，是否可以被视为真实。这一探讨引发了关于怀疑主义和知识基础的讨论。如果我们接受某些真理是不可证明的，那么我们必须处理这对我们理解现实及如何证明信念的影响。法律推理同样包含了provability的概念。在法庭上，举证责任在于提出主张的一方。法律标准通常要求以这样的方式呈现证据，以便被认为在合理怀疑之外是可证明的。这一provability的方面对于确保公正至关重要，并且判决必须基于坚实的证据而不是臆测。总之，provability是一个多面向的概念，超越了学科界限，并影响着各个研究领域。无论是在数学、计算机科学、哲学还是法律，理解provability的局限性和影响对于推动知识进步和确保系统与信念的完整性至关重要。随着我们继续探索知识的边界，追求provability将始终是一个核心主题，挑战我们批判性地思考我们能知道什么以及我们如何证明它。