BYOD stands for Bring Your Own Device. That is to utilize privately owned Smartphone and the like for "day-to-day operations".
Although it varies by the surveys, in Japan today, about 20% of companies "permit", 30% "prohibit", and the rest "abandon" BYOD. Also in United States, 80% of the companies "permit", and less than 10% "prohibit".
It is absurd that using own Smartphone "totally private only" nowadays. Sometimes you might catch an incoming "call" from the company to your private Smartphone. Then you ought to be allowed "mail checking" while on business trip or in transport. In my own opinion, to start with 'reading and writing email (Webmail)', 'checking the schedule', and 'processing tasks through the Workflow (especially on draft-approval)' should be allowed. Workers want it as well.
In the first place, in this "age of cloud", work style is changing rapidly, today. At this moment, the world economy has been sluggish, so we the human race must work harder. A radical revision of the business ought to be carried out more often though the policy settings to suit the business type × industries × scale is required. The world's GDP will be certainly improved, if they aggressively permit for example, 'working during move' or 'working at own home'.
Anyway, you should avoid 'ambiguous BYOD' (leaving as is). It will be ended up with increasing of 'secretly act' which you don't know whether it is iniquity or not, such as forwarding company business mails, or duplicating business data to USB memory or to Dropbox and so on. Rather, you should let "right thing to do" to be known, and let it penetrate as a rule.
[BYOD Application flow]