There is no logging persistence service in offline versions OH2b3 and OH2b4. Can it be installed manually? Did better ways to log selected item state changes appeared? Is it deprecated?
OH uses log4j instead of logback. Consequently the logging persistence addon is one of the few that are not supported by OH 2 at all. It is one of the four bindings known to be incompatible with OH 2 according to the docs.
I suppose no one has yet taken up the task to rewrite it to use log4j.
Short of creating some rules, or using MQTT Persistence and a script to write them out to file I don’t think there is an alternative at this time.