accordingly
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accordingly
Expresses a logical conclusion; consequently, therefore, accordingly. It introduces a sentence that follows from what was said previously.
Alle Flüge sind gestrichen, demnach müssen wir den Zug nehmen.
All flights have been canceled; accordingly, we have to take the train.
The word is made up of 'dem' (dative of 'das'/'der') and 'nach' (after/according to). Literally, it means something like 'after that' or 'as a result of that' and introduces a logical conclusion from something mentioned before.
Der letzte Bus ist schon gefahren. Demnach müssen wir ein Taxi rufen.
The last bus has already left. Accordingly, we have to call a taxi.
When 'demnach' (accordingly) comes at the beginning of the sentence (position 1), the verb follows directly in position 2 (inversion). However, it can also appear in the middle of the sentence after the verb and subject.
Demnach ist die Theorie falsch.
Accordingly, the theory is wrong.
'Demnach' (accordingly) is used mainly in written language or in formal spoken contexts such as news, reports, or presentations. It sounds factual and analytical.
Die Umfrageergebnisse sind eindeutig. Demnach wünscht sich die Mehrheit eine Veränderung.
The survey results are clear. Accordingly, the majority wants a change.
then
'dann' and 'demnach' can both express a result or conclusion. 'Dann' is broader and more everyday. It can mean a result from a condition or simply the next step. 'Demnach' is narrower: it means that something follows logically from a piece of information. The words can be confused when a consequence comes after a statement. If you mean a clear conclusion from facts, 'demnach' fits better. If you simply mean an everyday result, 'dann' is more natural.
Der Kunde hat schon bezahlt, demnach können wir die Ware heute verschicken.
The customer has already paid; accordingly, we can ship the goods today.
Wenn ihr den Termin nicht schafft, rufen wir dann morgen noch einmal an.
If you can't make the appointment, then we'll call again tomorrow.