V2EX universe of discourse

Universe of Discourse

释义 Definition

universe of discourse:在逻辑、数学、语言学与语义学中,指“讨论/推理所限定的对象范围”,也常译为论域讨论域。在这个范围内,量词(如 all, some)和谓词(如 is a student)所谈论的对象才被视为“可取值的对象”。(在不同语境下还可泛指“谈话所默认的范围”,但最常见用法是逻辑学意义。)

发音 Pronunciation (IPA)

/junvrs v dskrs/

例句 Examples

In this problem, the universe of discourse is all real numbers.
在这道题里,论域是所有实数。

If we change the universe of discourse from “people in this city” to “all people,” the statement may become false, because the quantifier now ranges over a much larger set.
如果我们把论域从“本市的人”改成“所有人”,这个陈述可能就变成假的,因为量词的取值范围扩大到了更大的集合。

词源 Etymology

该短语由 universe(“整体、全体;宇宙”)与 discourse(“论述、话语、讨论”)组合而成。其思想可追溯到传统逻辑与近代数理逻辑:为了避免歧义并明确“我们到底在哪些对象”,需要先规定一个“讨论的宇宙/范围”,也就是论域。

相关词 Related Words

文献与作品 Literary Works

  • Alfred Tarski, Introduction to Logic and to the Methodology of Deductive Sciences(逻辑学教材中常用该概念来限定解释范围)
  • W. V. O. Quine, Methods of Logic(讨论量化与解释时涉及论域/取值范围)
  • Herbert B. Enderton, A Mathematical Introduction to Logic(形式语义与模型论语境下系统使用“universe of discourse/ domain”)
  • Irving M. Copi, Introduction to Logic(在谓词逻辑部分讲解论域与量词的关系)
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