In formal logic and related branches of mathematics, a functional predicate, or function symbol, is a logical symbol that may be applied to an object term to produce another object term.Functional predicates are also sometimes called mappings, but that term has additional meanings in mathematics.In a model, a function symbol will be modelled by a function. Now consider a model of the formal language, with the types T and U modelled by sets [T] and [U] and each symbol X of type T modelled by an element [X] in [T].Then F can be modelled by the set
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| rdfs:label
| - Functional predicate (en)
- Predicato funzionale (it)
- Symbol funkcyjny (pl)
- 泛函谓词 (zh)
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| - Symbol funkcyjny – symbol używany w logice matematycznej i pokrewnych dziedzinach matematyki (np. algebrze abstrakcyjnej). Symbole funkcyjne są elementami alfabetów języków pierwszego rzędu (a także innych logik) i charakteryzują się tym, że zastosowane do obiektów zwanych termami produkują nowe termy. W potocznym języku matematyki, symbole funkcyjne w wyrażeniach matematycznych oznaczają funkcje, np.: w wyrażeniu symbolem funkcyjnym jest w jest nim +, w są nimi oraz (pl)
- 在形式逻辑和相关的数学分支中，泛函谓词或函数符号是应用于一个对象项而生成另一个对象项的。泛函谓词有时也叫做映射，但是这个术语还有其他意义。在模型中，函数符号被建模为函数。 特别是，在形式语言中的符号 F 是函数符号，如果给定任何表示在语言中的一个对象的符号 x，F(x) 也是表示这个语言中一个对象的符号。在有类型逻辑中，F 是带有域类型 T 和陪域类型 U 的函数符号，如果给定表示类型 T 的一个对象的任何符号 x，F(x) 也是表示类型 U 的对象的符号。你可以类似的定义多于一个变量的函数符号，类比于多于一个变量的函数；零 个变量的函数符号简单的是一个常量符号。 现在考虑这个形式语言的模型，它带有类型 T 和 U 被建模为集合 [T] 和 [U]，而类型 T 的每个符号 X 被建模为 [T] 中的元素 [x]。则 F 可以被建模为集合 它简单的是带有域 [T] 和陪域 [U] 的一个函数。[F(x)] = [F(y)] 只要 [x] = [y] 是一致性模型的要求。 (zh)
- In formal logic and related branches of mathematics, a functional predicate, or function symbol, is a logical symbol that may be applied to an object term to produce another object term.Functional predicates are also sometimes called mappings, but that term has additional meanings in mathematics.In a model, a function symbol will be modelled by a function. Now consider a model of the formal language, with the types T and U modelled by sets [T] and [U] and each symbol X of type T modelled by an element [X] in [T].Then F can be modelled by the set (en)
- In logica matematica, per predicato funzionale o formula funzionale o simbolo funzionale in si intende un predicato , in cui le variabili ed occorrono libere, avente la seguente proprietà: In altri termini, fissata una variabile della teoria o non esiste alcuna variabile della teoria che verifica il predicato oppure, se esiste una variabile che, insieme ad verifica , allora ogni altra variabile che verifica è necessariamente uguale ad . In altra maniera, fissata una generica variabile , esiste al più una variabile (ossia o non ne esiste alcuna oppure, se ne esiste una, allora ne esiste una sola) che verifica il predicato . (it)
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| - In formal logic and related branches of mathematics, a functional predicate, or function symbol, is a logical symbol that may be applied to an object term to produce another object term.Functional predicates are also sometimes called mappings, but that term has additional meanings in mathematics.In a model, a function symbol will be modelled by a function. Specifically, the symbol F in a formal language is a functional symbol if, given any symbol X representing an object in the language, F(X) is again a symbol representing an object in that language.In typed logic, F is a functional symbol with domain type T and codomain type U if, given any symbol X representing an object of type T, F(X) is a symbol representing an object of type U.One can similarly define function symbols of more than one variable, analogous to functions of more than one variable; a function symbol in zero variables is simply a constant symbol. Now consider a model of the formal language, with the types T and U modelled by sets [T] and [U] and each symbol X of type T modelled by an element [X] in [T].Then F can be modelled by the set which is simply a function with domain [T] and codomain [U].It is a requirement of a consistent model that [F(X)] = [F(Y)] whenever [X] = [Y]. (en)
- In logica matematica, per predicato funzionale o formula funzionale o simbolo funzionale in si intende un predicato , in cui le variabili ed occorrono libere, avente la seguente proprietà: In altri termini, fissata una variabile della teoria o non esiste alcuna variabile della teoria che verifica il predicato oppure, se esiste una variabile che, insieme ad verifica , allora ogni altra variabile che verifica è necessariamente uguale ad . In altra maniera, fissata una generica variabile , esiste al più una variabile (ossia o non ne esiste alcuna oppure, se ne esiste una, allora ne esiste una sola) che verifica il predicato . In maniera equivalente, un predicato in cui le variabili ed occorrono libere è funzionale in se (it)
- Symbol funkcyjny – symbol używany w logice matematycznej i pokrewnych dziedzinach matematyki (np. algebrze abstrakcyjnej). Symbole funkcyjne są elementami alfabetów języków pierwszego rzędu (a także innych logik) i charakteryzują się tym, że zastosowane do obiektów zwanych termami produkują nowe termy. W potocznym języku matematyki, symbole funkcyjne w wyrażeniach matematycznych oznaczają funkcje, np.: w wyrażeniu symbolem funkcyjnym jest w jest nim +, w są nimi oraz (pl)
- 在形式逻辑和相关的数学分支中，泛函谓词或函数符号是应用于一个对象项而生成另一个对象项的。泛函谓词有时也叫做映射，但是这个术语还有其他意义。在模型中，函数符号被建模为函数。 特别是，在形式语言中的符号 F 是函数符号，如果给定任何表示在语言中的一个对象的符号 x，F(x) 也是表示这个语言中一个对象的符号。在有类型逻辑中，F 是带有域类型 T 和陪域类型 U 的函数符号，如果给定表示类型 T 的一个对象的任何符号 x，F(x) 也是表示类型 U 的对象的符号。你可以类似的定义多于一个变量的函数符号，类比于多于一个变量的函数；零 个变量的函数符号简单的是一个常量符号。 现在考虑这个形式语言的模型，它带有类型 T 和 U 被建模为集合 [T] 和 [U]，而类型 T 的每个符号 X 被建模为 [T] 中的元素 [x]。则 F 可以被建模为集合 它简单的是带有域 [T] 和陪域 [U] 的一个函数。[F(x)] = [F(y)] 只要 [x] = [y] 是一致性模型的要求。 (zh)
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