There are no syntax errors with the formula but I don't believe it is performing the action desired. Typically, an OR statement compares two values and returns true or false...it is not a method of traversing a decision tree.
For example, if I had three color variables called RED BLUE and GREEN and wanted to return True if someone picked red or green, the formula would look like this:
IF ([BLUE] OR [GREEN])
Instead of OR, I would suggest using a IIF or IF THEN ELSE or if those don't work a CASE statement (note: case statements are resource-intensive and may cause performance issues if not optimized)
Check out this KB article: http://onlinehelp.tableau.com/current/pro/online/windows/en-us/help.htm#functions_functions_logical.html
Hope this helps!