Gum

Question

Originally someone asked if its mutar to chew gum on a fast day, and you responded, yes if you can chew all the sugar out prior to the fast, so then Joe followed up and asked about sugar free gum, and you said NO. If it would be ok if you were to remove all the sugar, why would sugarfree gum not be allowed? Also someone had told me that (I think its the Rama that talks about this) people used to suck on cinammon sticks on fast days, wouldn't sugar free gum be similar to that?