The ordinance excludes trespassers on the dog's property, in other words, the animal has a right to defend your home against intruders engaged in unlawful activity. Trespassers do not include anyone engaged in a lawful activity such as postal carriers, meter readers, visitors, or strangers knocking on your door for legitimate purposes. "Trespassers" also, importantly, do not include children running across the property line onto your property to get a ball, etc. In these situations, the animal should be restrained from contact as the owner is responsible for biting, attacks, etc. on their property and the dog could be categorized as vicious or potentially vicious.