File:Merge-arrow. svg It has been suggested that this article or section be merged into Entailment and Material conditional. Error creating thumbnail: Invalid Parameter - white This article needs additional citations for verification. File:Ambox style. png This article's citation style may be unclear. The references used may be made clearer with a different or consistent style of citation, footnoting, or external linking.

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dbpprop:abstract
  • File:Merge-arrow. svg It has been suggested that this article or section be merged into Entailment and Material conditional. Error creating thumbnail: Invalid Parameter - white This article needs additional citations for verification. File:Ambox style. png This article's citation style may be unclear. The references used may be made clearer with a different or consistent style of citation, footnoting, or external linking. In logic and mathematics, logical implication is a logical relation that holds between a set T of formulae and a formula B when every model (or interpretation or valuation) of T is also a model of B. In symbols, <math>T \models B</math>, <math>T \Rightarrow B</math> <math>T \therefore B</math> which may be read "T implies (entails) B, or "B is a (logical) consequence of T". In such an implication, T is called the antecedent, while B is called the consequent. In other words, (1) holds when the class of models of T is a subset of the class of models of B. Without using the language of models, (1) states that the material conditional formed from the conjunction of all the elements of T and B is valid. That is, it is valid that <math>(A_1\land\dots\land A_n)\to B</math>, where the Ai are the elements of T. (If T has infinite cardinality then, provided the language of T has the compactness property, some finite subset of T implies B. ) The statement in terms of the material conditional holds only in logics that have the semantic equivalent of the deduction theorem (and, as noted earlier, if T is infinite, then the compactness property is also required if the language disallows conjunctions over infinite sets of formulas). Thus, the original statement in terms of models is more general. The weaker truth function material implication, denoted by '→', should not be confused with the stronger logical implication.
  • En logique classique, l'expression « une proposition P implique logiquement une proposition Q » signifie « la proposition ¬P ∨ Q est vraie ». Formellement cela s'écrit P ⇒ Q. En logique intuitionniste, P ⇒ Q signifie que si l'on a une démonstration de P alors on a une démonstration de Q. Le symbole « ⇒ » s’appelle connecteur d’implication. « P ⇒ Q » s’appelle une implication logique.
  • Na lógica e na matemática, a implicação, ou condicional é a indicação do tipo "SE... ENTÃO", indicando que uma condição deve ser satisfeita necessariamente para que a outra seja verdadeira. Por exemplo, a expressão: "Se João esquia, Maria nada" é uma implicação. Na lógica booleana, as implicações retornam FALSO se, e somente se, o antecedente é VERDADEIRO e o conseqüente é FALSO.
  • Импликация — бинарная логическая связка, по своему применению приближенная к союзам «если… то…». Импликация записывается как посылка <math>\Rightarrow</math> следствие; применяются также стрелки другой формы и направленные в другую сторону (остриё всегда указывает на следствие). Суждение, выражаемое импликацией, выражается также следующими способами: Посылка является условием, достаточным для выполнения следствия; Следствие является условием, необходимым для истинности посылки.
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  • July 2008
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  • Talk:Logical implication Merger proposal
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  • File:Merge-arrow. svg It has been suggested that this article or section be merged into Entailment and Material conditional. Error creating thumbnail: Invalid Parameter - white This article needs additional citations for verification. File:Ambox style. png This article's citation style may be unclear. The references used may be made clearer with a different or consistent style of citation, footnoting, or external linking.
  • En logique classique, l'expression « une proposition P implique logiquement une proposition Q » signifie « la proposition ¬P ∨ Q est vraie ». Formellement cela s'écrit P ⇒ Q. En logique intuitionniste, P ⇒ Q signifie que si l'on a une démonstration de P alors on a une démonstration de Q. Le symbole « ⇒ » s’appelle connecteur d’implication. « P ⇒ Q » s’appelle une implication logique.
  • Na lógica e na matemática, a implicação, ou condicional é a indicação do tipo "SE... ENTÃO", indicando que uma condição deve ser satisfeita necessariamente para que a outra seja verdadeira. Por exemplo, a expressão: "Se João esquia, Maria nada" é uma implicação. Na lógica booleana, as implicações retornam FALSO se, e somente se, o antecedente é VERDADEIRO e o conseqüente é FALSO.
  • Импликация — бинарная логическая связка, по своему применению приближенная к союзам «если… то…».
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  • Logical implication
  • Implication (logique)
  • Implicação
  • Импликация
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