Interpreting the emotional response of others requires empathy which utilizes your emotions to feel others emotions. Logically define Love, hate, envy or any emotion, for the most part they only have emotional meaning. Emotions can be uses both ways as a deterrent but also as an emphasis.
Logically prove theft is wrong if you have need to survive and you aren't hurting anyone. Logically prove killing is wrong if it is legal to kill plants, animals, humans (that are bad), humans from another country we are at war with, humans that are innocent but near the enemy we are at war with. Don't forget criminals are employed by mobs and gangs today just to kill people even with all the social laws in place.
No one said anything about "right and wrong", which is, I think, where you're getting hung up. A completely logical perspective on anything need not consider "right and wrong", only what is or will be, and what is not or will not be.
So, take for instance, your claim that "Interpreting the emotional response of others requires empathy which utilizes your emotions to feel others emotions." I don't have to understand or even contemplate someone else's feelings to have the knowledge that if I hurt someone close to them, they may lash out at me. All this knowledge would require is an examination or witnessing of past events in which those bereaved or closest to the assailed sought vengeance, recompense or "justice". Something that happens all the time.
In thinking on pure logic alone, one would not need to "prove" that "theft is wrong" or "killing is wrong." I'm not even sure how you think that plays into any part of it. All you need know is the potential outcomes of your actions. You then take the action if the outcome is deemed worth the risk of possible detrimental consequences. Consequences that WILL BE FOISTED UPON YOU REGARDLESS YOUR ACCEPTANCE OF THEM.
Consider this line of thought: "If I steal this, I may be caught. If I am caught, I could go to prison, based on the consequences
those around me believe I should be bound by. Is this object worth stealing in my estimation?"
Here, the thinker contemplates the consequences, but not necessarily because he agrees with them or
feels anything at all about them - only because he knows them to be a factor/possibility/etc.