Lawyers for the city and the firefighters’ union will present their arguments before the state Appellate Court on May 24 on whether an issue over eight demoted fire captains goes to arbitration. Union President Daniel Daugherty said the Watertown Professional Fire Fighters Association Local 191 has been waiting for the case to move forward in the state Appellate Division, Fourth Department, in Rochester since last fall. In September, the city appealed State Supreme Court Judge James P. McClusky’s decision to allow the union to take the city to arbitration over the issue of the eight demoted captains.