The answer depends on what causes the deployment to break in your deployment.
If you have any of the following logging classes in your classpath that can cause logging to break: logging.properties, jboss-logging.properties, log4j.properties, log4j.xml, jboss-log4j.xml
So for example just run this code (either in your app or in a debugger) and it'll show you if you have the file in the classpath
getClass().getResource("/logging.properties")
Repeat for each of the log files specifed above, if any of those return non-null then you have found your culprit.
At that stage you can either remove the problem logging file, or alternatively use Rian's suggestion of adding <use-deployment-logging-config value="false"/>
(you don't need to use add-logging-api-dependencies in that scenario thou).
Another potential issue if you have multiple logging jar files. Keep in mind that wildfly will automatically provide several of those unless you use <add-logging-api-dependencies value="false"/>