App appears as Intalled when it's not

Hi

I have a MacBook Pro with two partitions in it´s Hard Disk, one with Snow Leopard and the other with Mountain Lion on it due to peripheals drivers compatibility.

Recently I bought Logic Pro from the APP STORE and installed it, when runing Snow Leopard, on it's partition.

Later I Started the computer with the Mountain Lion Partition and of course, Logic Pro wasn't in the Aplications Folder.

When I tried to download and install the app over Mountain Lion the App Store Application doesn´t let me do it and Logic Pro appears as "Installed"

I requested help to the App Store Help centre but they say that they can´t help me and sugest me to try it with the Logic Pro help (I really think that it is not related with LP but with App Store.

Any sugestion to install Logic Pro to run it with both OS's?

Thank you and sorry for my English that is not my mother laguage.