"This is not universally agreed-upon, but I use ..."

This is not universally agreed-upon, but I use "$~$A$~$ decides whether or not $~$B$~$ holds" to mean "$~$A$~$ outputs $~$1$~$ if $~$B$~$ holds, and outputs $~$0$~$ otherwise".

If I said "$~$A$~$ decides if $~$B$~$ holds", I would consider that ambiguous: it might mean "$~$A$~$ outputs $~$1$~$ if $~$B$~$ holds" without the requirement on $~$A$~$'s behaviour if $~$B$~$ doesn't hold.