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appy polly loggy 

Nadsat for 'Apology'.
appy polly loggy by MoonKnight March 13, 2003

appy polly loggies 

In Anthony Burgess's novella, A Clockwork Orange, it's the "nadsat" slang version of saying you're sorry. Synonymous with "apologies" as in "my apologies".
Oh, did I step on your foot? Appy polly loggies, O my Brother!