| dbo:abstract |
Formální teorie je jeden z nejdůležitějších pojmů matematickologické syntaxe. Mnoho matematických teorií může být formalizováno volbou vhodných axiomů. Některé teorie existují pouze jako teorie formální. Příkladem může být teorie množin, jejíž neformalizovaná podoba – tzv. naivní teorie množin je sporná. (cs) Στη μαθηματική λογική, μια θεωρία είναι σύνολο από σε μια τυπική γλώσσα. Για παράδειγμα, μια θεωρία πρώτης τάξης είναι σύνολο από προτάσεις πρώτης τάξης. Πολλοί συγγραφείς απαιτούν η θεωρία να είναι κλειστή ως προς τη λογική συνέπεια. (el) In der mathematischen Logik ist eine Theorie (der Prädikatenlogik erster Stufe) eine Menge von Aussagen über einer Signatur. (de) En lógica, una teoría es un conjunto de proposiciones dentro de un lenguaje formal que es semánticamente completo en el sentido de que todo modelo que satisface todas las proposiciones de la teoría también satisface cualquier otra proposición que sea consecuencia de la misma. Lo que diferencia a una teoría de un conjunto de proposiciones cualquiera es que incluye todas sus consecuencias, es decir, es un conjunto cerrado de proposiciones bajo el "operador consecuencia". (es) In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. In most scenarios, a deductive system is first understood from context, after which an element of a deductively closed theory is then called a theorem of the theory. In many deductive systems there is usually a subset that is called "the set of axioms" of the theory , in which case the deductive system is also called an "axiomatic system". By definition, every axiom is automatically a theorem. A first-order theory is a set of first-order sentences (theorems) recursively obtained by the inference rules of the system applied to the set of axioms. (en) Em lógica matemática, uma teoria (também chamada de teoria formal) é um conjunto de sentenças em uma linguagem formal. Normalmente um sistema dedutivo é entendido do contexto. Um elemento de uma teoria é chamado de axioma da teoria, e cada sentença que segue do axioma é chamado de teorema da teoria. Todo axioma também é um teorema. Uma teoria de primeira ordem é um conjunto de sentenças de primeira ordem. (pt) Teoria – niesprzeczny zbiór zdań. (pl) |
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June 2021 (en) |
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What if σ already contains all elements of A? (en) |
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Formální teorie je jeden z nejdůležitějších pojmů matematickologické syntaxe. Mnoho matematických teorií může být formalizováno volbou vhodných axiomů. Některé teorie existují pouze jako teorie formální. Příkladem může být teorie množin, jejíž neformalizovaná podoba – tzv. naivní teorie množin je sporná. (cs) Στη μαθηματική λογική, μια θεωρία είναι σύνολο από σε μια τυπική γλώσσα. Για παράδειγμα, μια θεωρία πρώτης τάξης είναι σύνολο από προτάσεις πρώτης τάξης. Πολλοί συγγραφείς απαιτούν η θεωρία να είναι κλειστή ως προς τη λογική συνέπεια. (el) In der mathematischen Logik ist eine Theorie (der Prädikatenlogik erster Stufe) eine Menge von Aussagen über einer Signatur. (de) En lógica, una teoría es un conjunto de proposiciones dentro de un lenguaje formal que es semánticamente completo en el sentido de que todo modelo que satisface todas las proposiciones de la teoría también satisface cualquier otra proposición que sea consecuencia de la misma. Lo que diferencia a una teoría de un conjunto de proposiciones cualquiera es que incluye todas sus consecuencias, es decir, es un conjunto cerrado de proposiciones bajo el "operador consecuencia". (es) In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. In most scenarios, a deductive system is first understood from context, after which an element of a deductively closed theory is then called a theorem of the theory. In many deductive systems there is usually a subset that is called "the set of axioms" of the theory , in which case the deductive system is also called an "axiomatic system". By definition, every axiom is automatically a theorem. A first-order theory is a set of first-order sentences (theorems) recursively obtained by the inference rules of the system applied to the set of axioms. (en) Em lógica matemática, uma teoria (também chamada de teoria formal) é um conjunto de sentenças em uma linguagem formal. Normalmente um sistema dedutivo é entendido do contexto. Um elemento de uma teoria é chamado de axioma da teoria, e cada sentença que segue do axioma é chamado de teorema da teoria. Todo axioma também é um teorema. Uma teoria de primeira ordem é um conjunto de sentenças de primeira ordem. (pt) Teoria – niesprzeczny zbiór zdań. (pl) |
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