To truncate a log you could use > logfilename. This is the old 'create a 0 size file trick'. Applied to a log file it'll truncate the log to zero size but won't remove the log so any logging routines will continue to work. If you rm a log file some loggers esp. in other unix's give up and stop logging rather than re-creating the log.
Regarding "what have logs got to do with security". If you regularly examine the logs for signs of faults or unusual behaviour (looking for open stable doors) that information is lost once the log is truncated.
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