It looks like it is CA Identity Manager question and you are trying to write a PX to send email.
I think Partially Completed is still considered as Completed from PX point of view. So you can trigger your PX on “Task Completion”. But if you want your PX to be only triggered for Partially Completed then you will have to put some filtering logic in PX. One way to differentiate Partially Complete and Complete is by their status in database. It is stored Task persistence database under table called TASKSESSION12_5 and column STATE. Its value for Complete is 128 and I think for Partially Complete is 1048576. Now You can write Entry rule in your PX and call SQL query to check STATE of task is 1048576 or not.
Please let me know if you need more with writing this PX.
Thanks,
Praveen Jain