I believe I have figured out the definition for love. It took me a long, long time to come up with this. It's not a sexy or romantic definition, it might not impress you. However, this is formal and I even have a proof for it.
The definition of love is extreme empathy.
The proof requires the premise that love is the opposite of hate. As we all know in competition, such as games or sports, your opponent takes action against you. This action causes hate. Even though you hate your opponent in the realm of the competition, outside of the competition the hate isn't there. Hate is the result of your opponent being antipathetic to your cause. Hate is then extreme antipathy. As there are only three options available: antipathy, apathy and empathy, and as love is the opposite of hate, love must therefore be extreme empathy. Apathy is of course no emotion so that can't be it. This I believe is the solution to a problem that has baffled man for centuries.