Substitution (logic) (original) (raw)
Substitution is a fundamental concept in logic.A substitution is a syntactic transformation on formal expressions.To apply a substitution to an expression means to consistently replace its variable, or placeholder, symbols by other expressions.The resulting expression is called a substitution instance, or instance for short, of the original expression.
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| dbo:abstract | Als Substitution bezeichnet man in der Logik allgemein die Ersetzung eines Ausdrucks durch einen anderen. Genauer müssen hier vier verschiedene Ausdrücke voneinander unterschieden werden: * das Substituendum (lat.: „das zu Ersetzende“): der Ausdruck, der ersetzt wird * das Substituens (lat.: „das Ersetzende“): der Ausdruck, der ersetzt * die Substitutions-Basis: der Ausdruck, in dem ersetzt wird * das Substitutionsresultat: das Ergebnis der Ersetzung. Beispiel: Ersetzen wir in dem Ausdruck (lies: „wenn , dann und “) den Ausdruck durch (lies: „ oder “), so erhalten wir: . Dabei ist Substituendum, Substituens, Substitutionsbasis und Substitutionsresultat. Man unterscheidet zwischen universeller und einfacher Substitution, außerdem ist in der Quantorenlogik auch der Begriff „frei zur Substitution“ von Bedeutung. (de) Substitution is a fundamental concept in logic.A substitution is a syntactic transformation on formal expressions.To apply a substitution to an expression means to consistently replace its variable, or placeholder, symbols by other expressions.The resulting expression is called a substitution instance, or instance for short, of the original expression. (en) 논리학에서 치환 실례(置換實例, 영어: substitution instance)는 명제를 구성하는 원자 명제를 다른 명제로 대신하여 얻는 명제이다. (ko) Substituição é um conceito fundamental em lógica.Uma substituição é uma transformação sintática em uma expressão formal.Aplicar uma substituição a uma expressão significa trocar uma variável ou símbolos por outras expressões.A expressão resultante é chamada de uma instância de substituição da expressão original (pt) |
| dbo:wikiPageExternalLink | https://web.archive.org/web/20180112160331/https:/pdfs.semanticscholar.org/28db/f1c89f36976bc41b38ff757991ca09e95524.pdf http://www.persee.fr/doc/phlou_0035-3841_1952_num_50_26_4394 |
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| dbp:id | substitution (en) |
| dbp:title | Substitution (en) |
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| rdfs:comment | Substitution is a fundamental concept in logic.A substitution is a syntactic transformation on formal expressions.To apply a substitution to an expression means to consistently replace its variable, or placeholder, symbols by other expressions.The resulting expression is called a substitution instance, or instance for short, of the original expression. (en) 논리학에서 치환 실례(置換實例, 영어: substitution instance)는 명제를 구성하는 원자 명제를 다른 명제로 대신하여 얻는 명제이다. (ko) Substituição é um conceito fundamental em lógica.Uma substituição é uma transformação sintática em uma expressão formal.Aplicar uma substituição a uma expressão significa trocar uma variável ou símbolos por outras expressões.A expressão resultante é chamada de uma instância de substituição da expressão original (pt) Als Substitution bezeichnet man in der Logik allgemein die Ersetzung eines Ausdrucks durch einen anderen. Genauer müssen hier vier verschiedene Ausdrücke voneinander unterschieden werden: * das Substituendum (lat.: „das zu Ersetzende“): der Ausdruck, der ersetzt wird * das Substituens (lat.: „das Ersetzende“): der Ausdruck, der ersetzt * die Substitutions-Basis: der Ausdruck, in dem ersetzt wird * das Substitutionsresultat: das Ergebnis der Ersetzung. Beispiel: Ersetzen wir in dem Ausdruck (lies: „wenn , dann und “) den Ausdruck durch (lies: „ oder “), so erhalten wir: . (de) |
| rdfs:label | Substitution (logic) (en) Substitution (Logik) (de) 치환 실례 (ko) Substituição (lógica) (pt) |
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