in parity there is a daemon
switch witch is useful but I can not find the logs in this mode.
Where does parity write the logs in daemon mode?
ethcore parity Issue 1560 reported that daemon was not logging and it was fixed in this commit
--log-file FILENAME Specify a filename into which logging should be
directed.
Use
parity daemon --log-file /path/to/parity.log
For different logging customizations check How to make parity write logs?