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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!
by vivovixivictum April 30, 2006
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Nadsat for an apology.

Nadsat is the language used by the main character and his friends in clockwork orange.
by Marc November 29, 2004
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