UIMA uses the standard java.util.logging (JUL). Most of my company's code used Apache Log4J, so we have a problem merging the messages from the two logging packages. Given that UIMA is now an Apache project, I think it makes sense that it work with Apache logging.
Two options occur to me:
1. Change all the logging calls in the code (perhaps Eclipse refactoring tools can help with that). Here's some discussion on migrating: http://www.oreillynet.com/onjava/blog/2005/12/migrating_from_jdk_logging_to.html
You could convert either to Log4J ( http://logging.apache.org/log4j/docs ) or to Apache Jakarta Commons Logging ( http://jakarta.apache.org/commons/logging ), which would allow UIMA to be configured to use either JUL or Log4J.
2. Write/find a JUL Handler that re-directs to Log4J. Here's an example: http://home.gwu.edu/~amrinder/chainsawHandler/UsingChainsawWithJDKLogging.html