You can sue the pit bull owner for negligence.  Negligence is the failure to exercise due care (that degree of care that a reasonable dog owner would have exercised under the same or similar circumstances to prevent foreseeable harm).If the dog has a history of biting/attacking, your lawsuit against the dog owner should include an additional claim which is strict liability.  Strict liability is liability whether or not due care was exercised.Your damages (monetary compensation you are seeking in your lawsuit) would be the value of your goat.  I know that may be difficult to ascertain especially considering the loss of your pet.Sorry to hear about this tragedy.