As used in this article, “public square” means any area or open space showing on a map or plat of a city, town, or village which has been filed or recorded in the office of the county clerk or county recorder of any county for more than fifty years and which is designated on the map or plat as a “square” or by other similar designation when no other words or insignia appear upon the map or plat showing the purposes for which the square may have been dedicated and when no deed, offer of dedication or other instrument appears of record in the office of the county recorder showing or indicating the purposes for which the same may have been dedicated.