A-Shell's primary log file—ashlog.log, typically in the %MIAME% directory—is self-maintaining. It rolls over to ashell.001, .002, .etc, up to a reasonable limit and then erases the older ones.
But in the UNIX environment, it does create one continuously growing log file, OPR:SPOOL.LOG, which records details of submissions to the system print queues. Depending on how much printing your application performs, you may want to set up a cron job to execute every so often to roll it over. See LOGROLL for a handy command for this purpose.