Logical thinking: Use of clear sound reasoning.
Logical emotions: The results of clear sound reasoning.
Remember on the old Star Trek episodes, when the Captain would be passionately losing it and Spock would be staring at him, calm as a cucumber? Kirk would wave a finger at his "damn logical, cold and unfeeling" self. One would assume that what Kirk was doing, having a huge tirade and flying off the handle was the normal reaction to a situation, and that Spock was somehow missing what it is to be human. That's not really the situation -
When we have illogical interpretations, assessments, and expectations, we end up with emotions that are out of control, stronger than is necessary. That is because the situation appears to be threatening some core beliefs we have about life, irrational beliefs such as; everyone should consider my well being when making decisions, things should be fair by my standards, if something goes wrong it has to be me that is the cause, if something happens then it will always happen....
With these unrealistic beliefs about how the world works, we often get ourselves overly upset. If someone doesn't send a thank you note for a gift, we might take it personally that they did not appreciate the gift or are not a kind person. Then, we become hurt or angry. When we accept the world in the random way it is, with everyone having free will, not always considering others, not aware of our needs or even caring about our needs, we let go of a lot of hurt, depression, anger, resentment, anxiety and more.
This is logic. Logic creates logical emotions.
If we explain the world as being random and being up to each individual to define, we must also allow other individuals to do it their own way, not our way. That's a scary thing to think, but consider this - the world was here long before you were born, it will be here long after you are gone. It is not up to the world to adjust to your presence, you must adjust to the world and the world is not going to consider you needs, you must do that. When you let go of unrealistic expectations, you also let go of out of proportion emotions.
Rather than black-and-white thinking, jumping to conclusions, or perfectionistic standards, if one adopts logical assessments of the reality of the world versus the world they think it should be, that person can get a great deal done in life without taking on the burden of personalizing it or expecting others to do it the "right way" (according to their own standards).
It is quite liberating to break down those cognitive distortions we have loaded our minds up with and learn to accept the reality of the world versus the world we wish it were.
I suggest the books below for helping to learn where you might be causing yourself undue stress and out of proportion emotional reactions. This is great for relieving everything from the burden of addictions to depression, anxiety, panic and more.
The New Guide to Rational Living by Albert Ellis and Robert Harper
The Feeling Good Handbook by David Burns
I Recovered From Panic Disorder by Sharon Day (Kindle)