Ubuntu mucks up the path for the log files to be written so by default it is trying to right them in the root directory and gets permission denied so you don't get any output. 

To fix it correct the path in the log4.properties file in your OpenVPMS install:

sudo nano /var/lib/tomcat6/webapps/openvpms/WEB-INF/classes/log4j.properties

Change log4j.appender.fileout.File=openvpms.log to log4j.appender.fileout.File=/var/lib/tomcat6/webapps/openvpms.log

and 

Change log4j.appender.fullout.File=openvpms-full.log to log4j.appender.fullout.File=/var/lib/tomcat6/webapps/openvpms-full.log

Now save your changes and restart tomcat and your log files should now be there.