Material implication (rule of inference) (original) (raw)
En lógica proposicional, la implicación material o definición del condicional es una regla de reemplazo válida que permite que una declaración condicional sea sustituida por una disyunción si y solo si el antecedente es negado. La regla establece que P implica Q es lógicamente equivalente a no-P o Q y puede sustituir a otra en demostraciones lógicas. Donde "" es un símbolo metalógico que representa "puede ser reemplazado en una demostración con."
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| dbo:abstract | En lógica proposicional, la implicación material o definición del condicional es una regla de reemplazo válida que permite que una declaración condicional sea sustituida por una disyunción si y solo si el antecedente es negado. La regla establece que P implica Q es lógicamente equivalente a no-P o Q y puede sustituir a otra en demostraciones lógicas. Donde "" es un símbolo metalógico que representa "puede ser reemplazado en una demostración con." (es) In propositional logic, material implication is a valid rule of replacement that allows for a conditional statement to be replaced by a disjunction in which the antecedent is negated. The rule states that P implies Q is logically equivalent to not- or and that either form can replace the other in logical proofs. In other words, if is true, then must also be true, while if is not true, then cannot be true either; additionally, when is not true, may be either true or false. Where "" is a metalogical symbol representing "can be replaced in a proof with," and P and Q are any given logical statements. To illustrate this, consider the following statements: * : Sam ate an orange for lunch * : Sam ate a fruit for lunch Then, to say, "Sam ate an orange for lunch" implies "Sam ate a fruit for lunch". Logically, if Sam did not eat a fruit for lunch, then Sam also cannot have eaten an orange for lunch (by contraposition). However, merely saying that Sam did not eat an orange for lunch provides no information on whether or not Sam ate a fruit (of any kind) for lunch. (en) Na lógica proposicional, implicação material é uma regra de substituição válida que permite que uma sentença condicional seja substituída por uma disjunção em que o antecedente é negado. A regra determina que P implica Q é logicamente equivalente à não-P ou Q e pode substituir o outro em provas lógicas. Onde ""é um símbolo metalógico que representa "pode ser substituído em uma prova." (pt) |
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| dbo:wikiPageRevisionID | 1094120052 (xsd:integer) |
| dbo:wikiPageWikiLink | dbr:Propositional_calculus dbr:Metalogic dbr:Antecedent_(logic) dbr:Validity_(logic) dbr:Material_conditional dbr:Negation dbr:Orange_(fruit) dbr:Contraposition dbr:Fruit dbr:Propositional_logic dbr:Statement_(logic) dbr:Symbol_(formal) dbr:Truth_table dbr:Law_of_excluded_middle dbr:Formal_proof dbr:Logical_disjunction dbr:Logical_equivalence dbc:Rules_of_inference dbc:Theorems_in_propositional_logic dbr:Rule_of_replacement |
| dbp:date | June 2022 (en) |
| dbp:field | dbr:Propositional_calculus |
| dbp:name | Material implication (en) |
| dbp:reason | This law doesn't hold in intuitionistic logic. If there is a proof of equiv that is accepted by intuitionists, it should be given here, instead of the current one. If not, the article should state that the equivalence doesn't hold in intuitionistic logic. (en) |
| dbp:statement | P implies Q is logically equivalent to not- or . Either form can replace the other in logical proofs. (en) |
| dbp:type | dbr:Rule_of_replacement |
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| dct:subject | dbc:Rules_of_inference dbc:Theorems_in_propositional_logic |
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| rdfs:comment | En lógica proposicional, la implicación material o definición del condicional es una regla de reemplazo válida que permite que una declaración condicional sea sustituida por una disyunción si y solo si el antecedente es negado. La regla establece que P implica Q es lógicamente equivalente a no-P o Q y puede sustituir a otra en demostraciones lógicas. Donde "" es un símbolo metalógico que representa "puede ser reemplazado en una demostración con." (es) Na lógica proposicional, implicação material é uma regra de substituição válida que permite que uma sentença condicional seja substituída por uma disjunção em que o antecedente é negado. A regra determina que P implica Q é logicamente equivalente à não-P ou Q e pode substituir o outro em provas lógicas. Onde ""é um símbolo metalógico que representa "pode ser substituído em uma prova." (pt) In propositional logic, material implication is a valid rule of replacement that allows for a conditional statement to be replaced by a disjunction in which the antecedent is negated. The rule states that P implies Q is logically equivalent to not- or and that either form can replace the other in logical proofs. In other words, if is true, then must also be true, while if is not true, then cannot be true either; additionally, when is not true, may be either true or false. * : Sam ate an orange for lunch * : Sam ate a fruit for lunch (en) |
| rdfs:label | Implicación material (es) Material implication (rule of inference) (en) Implicação material (regra de inferência) (pt) |
| owl:differentFrom | dbr:Material_inference |
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