Sometimes it is the smallest words which cause the biggest trouble.  Αφού (according to Stavropoulos, when, after as a temporal conjunction, and since, as as a causal conjunction) often requires a different translation in English.  Here are a few citations taken from the parallel corpus developed as part of the Lingua project (see here for details).

1  Τούτη η πράξη δεν ήταν παράνομη (τίποτα δεν ήταν παράνομο, αφού δεν υπήρχαν πια νόμοι) αλλά αν τον ανακάλυπταν ήταν σίγουρο πώς θα τον τιμωρούσαν με θάνατο, ή τουλάχιστο με είκοσι πέντε χρόνια καταναγκαστικά έργα This was not illegal (nothing was illegal, since there were no longer any laws), but if detected it was reasonably certain that it would be punished by death, or at least by twenty-five years in a forced-labour camp.
2  Στην πραγματικότητα δεν υπήρχε λέξη που να εκφράζει την "Επιστήμη", αφού κάθε έννοια που περιείχε αυτή η λέξη, καλυπτόταν με επάρκεια από τη λέξς Άγγσος There was, indeed, no word for "science", any meaning that it could possibly bear being already sufficiently covered by the word Ingsoc.
3  Πώς θα γίνει μεγάλος ζωγράφος, αφού δεν πόνεσε, δεν έζησε ... How can he become a great artist when he hasn't suffered, he hasn't lived...
4  "Αυτό που θέλω να πω είναι: γιατί να συνεχίζουν να ζουν μ'αυτούς αφού δεν τους ανδέχουν; What I say is, why go on living with them if they can't stand them?
5 Τότε προτιμώ τον Μαραγκό, αφού δεν έφαγε τόσα πολλά όσα η Φώκια. Then I like the Carpenter best - if he didn't eat as many as the Walrus.

One of these citations is from a Greek original, and the other four are from English originals.  Taking them in turn: 
1) is causal, and behaves according to the dictionary.
2) is causal, but note the non-finite participle construction in English (being ... covered).  This construction is often used in English to supply secondary information which relates to the main clause.  Note that this function is different from the function of an -οντας clause in Greek (which often expresses purpose rather than cause).
3) is also causal, but note the use of when in English, which can often have a causal sense as well as a purely temporal one (when it introduces "the reason for an opinion, comment or question" according to the Cobuild dictionary).  The sense is close to δεδομένου ότι ...
4) Is also causal.  The if introduces not a hypothetical situation, but a real one (it is a fact that they can't stand them).
5) As for 4.  Alice (for it is she) speaks as if she believes what she has just been told, that the Walrus ate more oysters than the Carpenter.  "If what you say, that he didn't eat so many, is true, then I like him better."

Note also that for 4 and 5, since could be substituted for if with no change in the attribution of causality.

Beyond all this, one further use of αφού is worth noting, which is particularly common in spoken Greek.  Here are two extracts from Greek government press briefings. In each case, αφού gives a reason, but what it is a reason for is not made explicit.

6  Θέλετε την άποψη τη δική μου, ως Υπουργού, για το συγκεκριμένο θέμα; Αφού απάντησα μόλις πριν.  Και είχα απαντήσει και παλαιότερα. [do you want my own opinion, as a minister?  "afou" I've just given an answer.  And I also answered it earlier]

 7  Α: Αυτό έχει γίνει μέχρι τώρα; Β: Έχει γίνει και γίνεται συνεχώς..  Α: Αφού δεν υπάρχει κανείς εκεί επάνω.  [A: Is that what has been happening up to now?  B:  Has been and still is.  A: "afou" there is nobody up there.

 In 6, the αφού-clause is an explanation of why the minister is not going to answer the question now (or again).  In 7, the fact that nobody is there is a reason for doubting the veracity of the previous statement.  ("Since there is nobody there, how are you able to make this assertion?")  In both examples, the αφού-clause has the function of an objection, and would have to be translated into English in a way that reflects this.  The commonest equivalent here is "but", and it is worth noting that typically in Greek, αφού in this usage can be preceded by μα. 

cf  Α: Διψάω!    Β: Αφού τώρα μόλις ήπιες [A:  I'm thirsty!  B:  But you've just had a drink!]

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