As Paddywak indicates, the date upon which a war ends can either be viewed as the date upon which hostilities cease or the date upon which a formal treaty is signed. It's the latter view which gives rise to the date of 1919 being used on monuments.
However, determining the end of a war by the date that a treaty is signed is unreliable if no formal treaty is actually signed. By that definition, Sudan and Lebanon are both still at war with Israel. North Korea is still officially at war with South Korea. And, going back to WWII, Russia is still officially at war with Japan! (There are several web references to individual towns and cities remaining at war with entire nations. For example, Berwick appears to be at war with Russia! I've no idea which conflict that refers to, but there are plenty of websites which seem to believe it).
Chris