The Tree of Logic, also known as the third tree of Eden, releases an aroma that causes whomever is around it to become cold and hard hearted. This was done primarily so the Blue Djinn of Babylon would be beyond good and evil and treat all disputes equally between. All previous Blue Djinn had to undergo this process before Faustina Sachertorte found a way to bypass this.
Once a year, it was required for the Blue Djinn to spend thirty days in the Hanging palace in which she is exposed to the aroma. Other people who enter are affected as well even if they are not the blue djinn. When Philippa stayed with Ayesha at her home, she was similarly affected by the "hard-heartedness" though it was reversed when John and Nimrod arrived to try and rescue her.
Ayesha explained that once they were three trees of Adam and Eve, one the tree of knowlege, and the other of tree and life. In some versions, the tree of logos, or logic is mentioned and she believed it came from the garden.
The air of the palace is infused with the scent of the tree's blossom. the food and water prepared also includes blossoms of the tree so that it would be nearly impossible for any person within the Palace of the Blue Djinn to resist. Even after she left the palace, Philippa said she still had tendencies to blurt out the "logical" answer from time to time.