Ive heard that the owners of a cat cant sue can we?

not sure if you read my bit bout my dogs killing a cat on our property were our dogs were confined. the cat entered our premises while we were out. next door neighbours saw and heard most of it so we have witnesses. the cat was not savaged jst scared to death i think. we told the owners and give them their cat. they are telling everyone our dogs are vicious and will hurt anyone cause there are a staffi and a american bulldog. if anyone knew our dogs they would knowe there big softies. can we sue them for definiation of character on our dogs? (slander) and for the cat entering our property and the stress of them trying to put our dogs down. the owners have been very threating towards us as well.