Airedales as a breed were designed to have high prey drives and worked to eliminate predators for their owners. This is not aggression its a drive issue and a lack of training and socialization to permit the dog to comprehend the kittens as 'pack mates'.
You can read about breed traits in this breed here
http://www.lovemypet.com.au/advice/dogbreeds/airedaleterrier.htm
cat killing is a really common behavior in this breed.
So sorry for your loss and I hope this helps you!
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