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单词 Logical quantifier
释义

Logical quantifier

中文百科

量化 (数理逻辑) Quantifier (logic)

(重定向自Logical quantifier)
展示范围和变量捕获的语法树

在语言和逻辑中,量化是指定一个谓词的有效性的广度的构造,就是说指定谓词在一定范围的事物上成立的程度。产生量化的语言元素叫做量词。结果的句子是量化的句子,我们称我们已经量化了这个谓词。量化在自然语言和形式语言中都使用。在自然语言中,量词的例子有“所有”、“某些”;“很多”、“少量”、“大量”也是量词。在形式语言中,量化是从旧公式产生新公式的公式构造子(constructor)。语言的语义指定了如何把这个构造子解释为一个有效性的广度。量化是变量约束操作的实例。

在谓词逻辑的两类基本量化是全称量化和存在量化。这些概念被更详细的叙述于在单独文章中;下面我们讨论适用于二者的特征。其他种类的量化包括唯一量化。

英语百科

Quantifier (logic) 量化 (数理逻辑)

(重定向自Logical quantifier)
Syntactic tree illustrating scope and variable capture

In logic, quantification is a construct that specifies the quantity of specimens in the domain of discourse that satisfy an open formula.

For example, in arithmetic, it allows the expression of the statement that every natural number has a successor. A language element which generates a quantification (such as "every") is called a quantifier. The resulting expression is a quantified expression, it is said to be quantified over the predicate (such as "the natural number x has a successor") whose free variable is bound by the quantifier. In formal languages, quantification is a formula constructor that produces new formulas from old ones. The semantics of the language specifies how the constructor is interpreted. Two fundamental kinds of quantification in predicate logic are universal quantification and existential quantification. The traditional symbol for the universal quantifier "all" is "∀", a rotated letter "A", and for the existential quantifier "exists" is "∃", a rotated letter "E". These quantifiers have been generalized beginning with the work of Mostowski and Lindström.

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更新时间:2025/6/23 11:30:09