If the pet in question is running amok in your yard where your pet is properly secured I do not see a problem. If you pet is in the other pet's yard then your pet is in the wrong.

I ride my bike with my pet all the time and get chased from dogs who the owner's think will not chase. The owners look so stupid cause they are yelling and shit and thier dogs ignore them. I ride just fast enough to keep the pet just off my dog's tail and sometimes they follow for a half mile or more. Stupid pet owners should keep thier pets secure. Now they gotta hope thier pet knows the way home or gotta look for it.  Just incase I ever find a dog who can keep up with a Border Collie tied to a 24 speed bicycle I am always packin.  It's funny to watch the dog try to catch us then when it gets close it has to try and run or bite. If it tries to bite it misses a couple steps and we gain distance and the chase starts again.