Deductive closure (original) (raw)
In mathematical logic, a set of logical formulae is deductively closed if it contains every formula that can be logically deduced from , formally: if always implies . If is a set of formulae, the deductive closure of is its smallest superset that is deductively closed. The deductive closure of a theory is often denoted or . This is a special case of the more general mathematical concept of closure — in particular, the deductive closure of is exactly the closure of with respect to the operation of logical consequence.
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| dbo:abstract | In mathematical logic, a set of logical formulae is deductively closed if it contains every formula that can be logically deduced from , formally: if always implies . If is a set of formulae, the deductive closure of is its smallest superset that is deductively closed. The deductive closure of a theory is often denoted or . This is a special case of the more general mathematical concept of closure — in particular, the deductive closure of is exactly the closure of with respect to the operation of logical consequence. (en) In de logica is de deductieve afsluiting van een verzameling proposities en een verzameling afleidingsregels de verzameling proposities zodanig dat deze elke propositie bevat die afleidbaar is uit met regels in . Formeel beschouwd is de deductieve afsluiting een afsluiting waarbij een verzameling proposities gesloten is onder afleidingsregels in . Binnen de kennistheorie wordt gediscussieerd of bepaalde deelverzamelingen van kennis, die bijvoorbeeld betrekking hebben op kennis of geloof over een bepaald onderwerp, afgesloten zijn onder deductie. (nl) In matematica la chiusura deduttiva consiste nell'insieme di deduzioni che possono essere ricavate a partire da un insieme di assiomi. In altre parole, la chiusura deduttiva è l'insieme di tutte le formule che, tramite le regole di inferenza disponibili, sono conseguenza dell'insieme di assiomi considerato. In termini più formali, sia l'insieme di formule considerato, la sua chiusura deduttiva viene indicata con . (it) Fecho dedutivo é uma propriedade de um conjunto de objetos (normalmente sentenças lógicas). Consideramos que um conjunto de objetos B possui fecho dedutivo ou é fechado sob uma determinada operação de consequência C se, para cada subconjunto B' de B, se B' se relaciona com um conjunto de objetos D através de C, então D é subconjunto de B. No contexto de lógica, o fecho lógico de um conjunto de sentenças B é o conjunto de todas as sentenças que podem ser deduzidas a partir de B. (pt) |
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| rdfs:comment | In mathematical logic, a set of logical formulae is deductively closed if it contains every formula that can be logically deduced from , formally: if always implies . If is a set of formulae, the deductive closure of is its smallest superset that is deductively closed. The deductive closure of a theory is often denoted or . This is a special case of the more general mathematical concept of closure — in particular, the deductive closure of is exactly the closure of with respect to the operation of logical consequence. (en) In de logica is de deductieve afsluiting van een verzameling proposities en een verzameling afleidingsregels de verzameling proposities zodanig dat deze elke propositie bevat die afleidbaar is uit met regels in . Formeel beschouwd is de deductieve afsluiting een afsluiting waarbij een verzameling proposities gesloten is onder afleidingsregels in . Binnen de kennistheorie wordt gediscussieerd of bepaalde deelverzamelingen van kennis, die bijvoorbeeld betrekking hebben op kennis of geloof over een bepaald onderwerp, afgesloten zijn onder deductie. (nl) In matematica la chiusura deduttiva consiste nell'insieme di deduzioni che possono essere ricavate a partire da un insieme di assiomi. In altre parole, la chiusura deduttiva è l'insieme di tutte le formule che, tramite le regole di inferenza disponibili, sono conseguenza dell'insieme di assiomi considerato. In termini più formali, sia l'insieme di formule considerato, la sua chiusura deduttiva viene indicata con . (it) Fecho dedutivo é uma propriedade de um conjunto de objetos (normalmente sentenças lógicas). Consideramos que um conjunto de objetos B possui fecho dedutivo ou é fechado sob uma determinada operação de consequência C se, para cada subconjunto B' de B, se B' se relaciona com um conjunto de objetos D através de C, então D é subconjunto de B. No contexto de lógica, o fecho lógico de um conjunto de sentenças B é o conjunto de todas as sentenças que podem ser deduzidas a partir de B. (pt) |
| rdfs:label | Deductive closure (en) Chiusura deduttiva (it) Deductieve afsluiting (nl) Fecho dedutivo (pt) |
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