Two things, if you mean the quest log in the GUI interface, that is a place for you to write notes on quests, it isn't automatically filled with information.
Also, you can find logs of your conversations with npc's/players/etc stored locally on your computer if you must log out before finishing a quest. Common locations listed below:
Windows: In the user home directory, usually in "Document and Setting\Username\Application Data\PlaneShift
Linux: ~/.PlaneShift
Mac OS X: ~/Library/Application Support/PlaneShift