Concept
The concept of this motto is quite simple: You believe that you have already met the love of your life, but for some reason or other you two are apart. Betray your heart with logic offers two possibilities: Either you are destined for each other, then you will end up together sooner or later. Or you can't be happy together, which means that it was never meant to be in the first place.
It's all about telling yourself that, no matter how bad it is, everything will turn out right.

Foundation
Betray your heart with logic is based on the following beliefs: Since you are saying that you know the love of your life lets assume that you believe in some kind of fate, because if someone is meant for you, there has to be something to affect that. And as the world needs some optimism lets trust that fate is kind and not cruel, meaning that it will never be possible that the love of your life will not love you in return.

Problem
The problem which called to life this concept is quite a common one. You met the love of your life. You had a wonderful time together. Then they broke up, because your love thinks they don't love you. Now, after weeks of tearful nights and days it's time for you to move on.

How to Survive

Step 1: Be Sure.
Whatever you do after being left behind, be sure that you do it because it is best for you. There will be lots of people, friends and family and maybe others as well, to give you advice. They may try to force you to do something. But whatever they think and say, the only important thing is that you feel comfortable with what you do next. It is your life, and your happiness depends on your personality.
Here's an easy way to settle for one of two options: toss a coin. If you agree with the outcome, stick to it. If it makes you feel uneasy, go for the other option. Because the coin doesn't know what's right, but your subconscious does.

Step 2: Friendship.

"The worst form of missing someone is knowing that the person right next to you will never belong to you."

You might want to be friends with the love of your life. They mean a lot to you, so why not? But keep in mind that, no matter how much you love them, they stopped loving you. Sooner or later you'll have to cope with them in a new relationship. No one can hold it against you when you're not strong enough for that. Never forget to do what is best for you. Maybe you have to try both friendship and no contact to find out what makes you feel more at ease.

Step 3: A New Love.
For some people, finding a new love isn't difficult. If you are falling in love again, go for it. The time that passed since the supposed love of your life broke up with you doesn't matter. What others think about that also doesn't matter. Your heart is making the decision here, that is the important part.
For others it is harder. They are fixated on the one who left them. They had already built their future around this person. If you are one of those, take your time. Nobody can force your heart to open up again. Being with the wrong person because others want you to probably won't make you happy. Remember to care for yourself first, then think of others. Sometimes it only works this way.

Rules
You are free to decide whether or not you believe this. But if you choose to trust in Betray your heart with logic then you should know some general rules, just to make sure there'll be no misunderstandings.

1. Listen.
The first and most important rule is that you listen to your heart. In German the heart is "knocking", not "beating" and there is an advice saying "Next time your heart knocks, just let it in". So listen to your heart, for that and your gut instinct know what is right. And only they know who your true love is.

2. Fight.
Even though the concept says when you can't be happy together it isn't meant to be, you are not allowed to sit back and wait for your love to come to you. Fate needs help, but don't do anything rash. Never forget to listen. Sometimes it really is better to wait as to not hurt somebody. You need to be sure that this is the love of your life. You shall fight, at the right time and with the right weapons. Your heart will tell you all about that. Take a moment to relax, let your heart speak to you, think about what you learned. Sleep on it. In the morning you'll know what is the right thing to do. Try to be sure, even though there might not be an absolute certainty.

3. Don't be afraid.
Fear is an instrument evolution gave us to protect our lives when it comes to dangerous animals or situations. But normally love won't kill you. It might hurt you and maybe you tend to seeing it as an enemy. But you want the love of your life in your life. Therefore you can't run away from love. When you decide about how to fight, don't let fear delay your decision and don't let it interfere with it. You will do the wrong thing out of fear, because it will silence your heart and gut instinct.

Appendix
Although the word "logic" is part of the motto itself, you might have noticed that the concept advises you to listen to your heart, which tends to be more on the illogical side. But without a heart, love does not work. Betray your heart with logic means to say that the pain of a broken heart is easier to bear when you believe that there is hope. The aching heart will tell you that everything is lost. But it is not. There is a part of your heart which does not ache. This is what you need to find and listen to.

Betray your heart with logic is always open for interpretation.
There is no claim that there is only one person meant for you.
No one says you can't be happy again if your loved one died.
The purpose of this concept is to give hope. It cannot heal a broken heart, but it can strengthen a person. It encourages to carry on, to find a new love or to fight for the one already known. It wants you to take matters into your own hands. Consider the possibility that you were wrong thinking you've already found the right person. But most of all, Betray your heart with logic ought to remind you that your heart is your unimpeachable advisor when it comes to love and that fate, no matter how much it hurts, does not tantalise you for fun.
Have faith.