There is no such thing as logical empathy. Empathy is the ability to perceive someone else's emotional state. i.e. putting yourself in someone's shoes.
Empathy isn't just perceiving emotional states but actually mirroring the emotions of the other person. Feeling emotions "for" the other person. (E.g., feeling "sad for" someone.)
What's being called "logical empathy" here is the perception/understanding that you're calling empathy.