Without emotion, it turns out that you have a *very* hard time reaching some kinds of conclusion. Example One: A man who suffered an injury to the area of the brain that is the seat of emotion duly lost the ability to “feel” – no more sad, no more happy. He went to the grocery store to buy cookies to feed guests, and spent hours looking at all the varieties. Nothing he saw moved him to spend money.
You can still solve a sudoku or do a crossword puzzle or figure out your taxes. You may still be able to hold a job. The “processing of logic” in the driest sense has nothing to do with emotion. But deciding between alternatives based on feeling, e.g. how the cookie is going to taste, is *tough*.
The other extreme is when emotion bleeds over, and you encounter a logic problem where deep emotion connects to the various possible conclusions. In this case, emotion not only enables a choice that requires feeling, it zeroes in on the choice that reinforces a feeling. Logic can go out the window, even become a servant of emotion directed at constructing a seemingly logical structure which also just happens to support the emotionally satisfying conclusion.
Yes, emotion interferes with the processing of logic. Absolutely. But it’s also a critical part of making far more life choices than you’d suspect.