Its hard to say if your terrier is a jack, rat or parson, they all look very similar. All terriers were bred to hunt varmints of one sort or another. I have Scottish terriers and they are great at keeping the rodent population down around the farm. They have killed kittens, baby chicks and adult chickens although they do leave my adult house cat alone. I'm not saying all terriers are automatic killers but they are bred to do this. Just be careful what you let him have access too. Watch out for the tom cat too, I know my tom cat in the barn will kill all male kittens. So if one or two come up dead don't automaticly blame the dog.
"Until one has loved an animal, part of one's soul remains unawakened..."
- Anatole France