What Discmania has to say about the Logic:

 
The Logic has a low-profile ergonomic grip designed to fit a variety of preferences when it comes to hand feel. The slightly rounded will feel very comfortable in hand and release effortlessly every time. Players that find the P2 or Link to be a bit too deep will surely enjoy how easy a logic is to grip and control. Our goal was to create something that is very responsive to minor adjustments for all types of throws and won’t burn you if you over-correct too much.
 
As a straighter flying putter compared to the Link, this beadless design allows for an equal amount of glide but will offer an easier trajectory for any player on any line you want to throw it on. Although it’s designed as a putt and approach disc, many players are going to be reaching for this one off the tee as well. 

About the plastic:

Soft Exo: The Soft Exo plastic gives players the option of a softer putter for both throwing and putting. You'll find that the plastic of these Soft Logics has a bit more grip to the plastic and the slightly gummier composition allows grab a hold of the chains and the surrounding green without sliding or skipping away. A truly useful tool to have for those tricky landscapes out there!
 
Good for: Control drives, Circle 1 & 2 putts, Scramble shots