Structure (mathematical logic) (original) (raw)
Model (také struktura) je matematický pojem z oblasti matematickologické sémantiky. Je to seskupení objektů, na němž jsou definovány nějaké vztahy (relace) a přiřazení (funkce) tak, že vytváří „realizaci“ nějaké formální teorie.
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| dbo:abstract | Model (také struktura) je matematický pojem z oblasti matematickologické sémantiky. Je to seskupení objektů, na němž jsou definovány nějaké vztahy (relace) a přiřazení (funkce) tak, že vytváří „realizaci“ nějaké formální teorie. (cs) Der Begriff der Struktur (englisch (first order) structures) ist ein Grundbegriff der mathematischen Teilgebiete der Modelltheorie und der universellen Algebra. Eine Struktur ist dabei eine Menge, genannt Universum der Struktur, versehen mit Operationen auf dieser Menge. Eine Vielzahl mathematischer Strukturen (als informeller Begriff) lässt sich als eine solche Struktur auffassen, insbesondere jede algebraische Struktur und jede Ordnungsstruktur. Ein Beispiel für eine Struktur sind die natürlichen Zahlen versehen mit der Addition, der Multiplikation und dem Vergleich . In der Modelltheorie werden Strukturen mitunter auch Modelle genannt. (de) En álgebra universal y en teoría de modelos, una estructura consiste en una colección de elementos acompañada a su vez por una colección de funciones y relaciones finitas definidas en ella.El álgebra universal estudia estructuras que generalizan las estructuras algebraicas tales como grupos, anillos, campos, retículos y espacios vectoriales. El término álgebra universal es usado para estructuras sin símbolos de relaciones. La teoría de modelos tiene un alcance diferente que abarca teorías más arbitrarias, incluyendo estructuras más fundamentales como modelos de la teoría de conjuntos. Desde el punto de vista modelo-teórico, las estructuras son objetos usados para definir la semántica de lógicas de primer orden. * Datos: Q1851710 (es) En logique mathématique, plus précisément en théorie des modèles, une structure est un ensemble muni de fonctions et de relations définies sur cet ensemble. Les structures usuelles de l'algèbre sont des structures en ce sens. On utilise également le mot modèle comme synonyme de structure (voir ). La sémantique de la logique du premier ordre se définit dans une structure. (fr) Dalam aljabar universal dan dalam teori model, struktur terdiri dari himpunan bersama dengan kumpulan operasi finiter dan relasi yang ditentukan di atasnya. Struktur studi aljabar universal yang menggeneralisasi struktur aljabar seperti grup, gelanggang, bidang dan ruang vektor. Istilah aljabar universal digunakan untuk struktur tanpa . Teori model memiliki cakupan berbeda yang mencakup teori yang lebih sewenang-wenang, termasuk struktur seperti model teori himpunan. Dari sudut pandang model-teori, struktur adalah objek yang digunakan untuk mendefinisikan semantik . Untuk teori tertentu dalam teori model, struktur disebut model 'jika memenuhi aksioma yang menentukan teori itu, meskipun kadang-kadang disamarkan sebagai ketika seseorang membahas gagasan dalam pengaturan yang lebih umum dari model matematika. Ahli logika terkadang menyebut struktur sebagai . Dalam , struktur tanpa fungsi dipelajari sebagai model database relasional, dalam bentuk model relasional. (in) In universal algebra and in model theory, a structure consists of a set along with a collection of finitary operations and relations that are defined on it. Universal algebra studies structures that generalize the algebraic structures such as groups, rings, fields and vector spaces. The term universal algebra is used for structures with no relation symbols. Model theory has a different scope that encompasses more arbitrary theories, including foundational structures such as models of set theory. From the model-theoretic point of view, structures are the objects used to define the semantics of first-order logic. For a given theory in model theory, a structure is called a model if it satisfies the defining axioms of that theory, although it is sometimes disambiguated as a semantic model when one discusses the notion in the more general setting of mathematical models. Logicians sometimes refer to structures as "interpretations", whereas the term "interpretation" generally has a different (although related) meaning in model theory, see interpretation (model theory). In database theory, structures with no functions are studied as models for relational databases, in the form of relational models. (en) 모형 이론에서 구조(構造, 영어: structure)는 어떤 주어진 1차 논리 언어의 해석을 갖춘 집합이다. (ko) Un modello, nella logica matematica, è un sistema constituito da formule logiche che descrivono i fenomeni in un determinato ambiente di riferimento. Sebbene la seguente definizione faccia riferimento alla teoria dei modelli, gli esempi e le definizioni successive fanno riferimento a teoria e logica del primo ordine. (it) Na lógica, uma estrutura (ou estrutura de interpretação) é um objeto que dá significado semântico ou interpretação aos símbolos definidos pela assinatura de uma linguagem. Uma estrutura possui diferentes configurações, seja em lógicas de primeira ordem, seja em linguagens lógicas poli-sortidas ou de ordem superior. (pt) 在数学学科模型论中，语言 的结构 (也叫做 '-结构'，并通常写为哥特体大写)是一个有序对，它的第一个成员是论域或全集 (对应于可能带有定义在其上的关系和函数的集合，并通常写为相应于结构名字的罗马体大写)，它的第二个成员是一个释义 ，就是 的一个偏函数，它完全定义在 的之上，使得 的常量符号对应于 上的元素，如果有的话； 的函数符号对应于 上的函数，如果有的话；而 的关系符号对应于 上的关系；如果有的话。 (zh) |
| dbo:wikiPageExternalLink | http://www.math.uni-hamburg.de/home/diestel/books/graph.theory/ https://archive.org/details/courseinmodelthe0000poiz https://archive.org/details/mathematicallogi1996ebbi https://archive.org/details/modeltheory0000hodg http://www.thoralf.uwaterloo.ca/htdocs/ualg.html http://plato.stanford.edu/entries/logic-classical/%234 http://plato.stanford.edu/entries/logic-classical/ http://plato.stanford.edu |
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| dbp:date | November 2022 (en) |
| dbp:reason | "Interpretation" seems to be used with slightly different meanings in model theory versus other areas of mathematical logic, and to a beginner it is not necessarily entirely clear which sense is meant here. It appears to be the sense corresponding to "interpretation function" defined in the section below, but if so that is somewhat confusing, because the notion of "interpretation function" has not yet been defined in the article here yet is already being referenced. There may be a way to phrase this so that it is also clearer to beginners. (en) |
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| rdfs:comment | Model (také struktura) je matematický pojem z oblasti matematickologické sémantiky. Je to seskupení objektů, na němž jsou definovány nějaké vztahy (relace) a přiřazení (funkce) tak, že vytváří „realizaci“ nějaké formální teorie. (cs) Der Begriff der Struktur (englisch (first order) structures) ist ein Grundbegriff der mathematischen Teilgebiete der Modelltheorie und der universellen Algebra. Eine Struktur ist dabei eine Menge, genannt Universum der Struktur, versehen mit Operationen auf dieser Menge. Eine Vielzahl mathematischer Strukturen (als informeller Begriff) lässt sich als eine solche Struktur auffassen, insbesondere jede algebraische Struktur und jede Ordnungsstruktur. Ein Beispiel für eine Struktur sind die natürlichen Zahlen versehen mit der Addition, der Multiplikation und dem Vergleich . In der Modelltheorie werden Strukturen mitunter auch Modelle genannt. (de) En logique mathématique, plus précisément en théorie des modèles, une structure est un ensemble muni de fonctions et de relations définies sur cet ensemble. Les structures usuelles de l'algèbre sont des structures en ce sens. On utilise également le mot modèle comme synonyme de structure (voir ). La sémantique de la logique du premier ordre se définit dans une structure. (fr) 모형 이론에서 구조(構造, 영어: structure)는 어떤 주어진 1차 논리 언어의 해석을 갖춘 집합이다. (ko) Un modello, nella logica matematica, è un sistema constituito da formule logiche che descrivono i fenomeni in un determinato ambiente di riferimento. Sebbene la seguente definizione faccia riferimento alla teoria dei modelli, gli esempi e le definizioni successive fanno riferimento a teoria e logica del primo ordine. (it) Na lógica, uma estrutura (ou estrutura de interpretação) é um objeto que dá significado semântico ou interpretação aos símbolos definidos pela assinatura de uma linguagem. Uma estrutura possui diferentes configurações, seja em lógicas de primeira ordem, seja em linguagens lógicas poli-sortidas ou de ordem superior. (pt) 在数学学科模型论中，语言 的结构 (也叫做 '-结构'，并通常写为哥特体大写)是一个有序对，它的第一个成员是论域或全集 (对应于可能带有定义在其上的关系和函数的集合，并通常写为相应于结构名字的罗马体大写)，它的第二个成员是一个释义 ，就是 的一个偏函数，它完全定义在 的之上，使得 的常量符号对应于 上的元素，如果有的话； 的函数符号对应于 上的函数，如果有的话；而 的关系符号对应于 上的关系；如果有的话。 (zh) En álgebra universal y en teoría de modelos, una estructura consiste en una colección de elementos acompañada a su vez por una colección de funciones y relaciones finitas definidas en ella.El álgebra universal estudia estructuras que generalizan las estructuras algebraicas tales como grupos, anillos, campos, retículos y espacios vectoriales. El término álgebra universal es usado para estructuras sin símbolos de relaciones. La teoría de modelos tiene un alcance diferente que abarca teorías más arbitrarias, incluyendo estructuras más fundamentales como modelos de la teoría de conjuntos. Desde el punto de vista modelo-teórico, las estructuras son objetos usados para definir la semántica de lógicas de primer orden. (es) Dalam aljabar universal dan dalam teori model, struktur terdiri dari himpunan bersama dengan kumpulan operasi finiter dan relasi yang ditentukan di atasnya. Struktur studi aljabar universal yang menggeneralisasi struktur aljabar seperti grup, gelanggang, bidang dan ruang vektor. Istilah aljabar universal digunakan untuk struktur tanpa . Dalam , struktur tanpa fungsi dipelajari sebagai model database relasional, dalam bentuk model relasional. (in) In universal algebra and in model theory, a structure consists of a set along with a collection of finitary operations and relations that are defined on it. Universal algebra studies structures that generalize the algebraic structures such as groups, rings, fields and vector spaces. The term universal algebra is used for structures with no relation symbols. In database theory, structures with no functions are studied as models for relational databases, in the form of relational models. (en) |
| rdfs:label | Model (logika) (cs) Struktur (erste Stufe) (de) Estructura (lógica) (es) Structure (logique mathématique) (fr) Struktur (logika matematika) (in) Modello (logica matematica) (it) 구조 (논리학) (ko) Estrutura de interpretação (lógica) (pt) Structure (mathematical logic) (en) 结构 (数理逻辑) (zh) |
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