Nowadays, there are only 3 common types of regimes, regardless of a country's official title: democracy, dictatorship, and "Constitutional Monarchies", which are basically democracies with a monarch who has little/symbolic control in the country that they represent.
There is another, more uncommon regime that has largely become a thing of the past, called "Absolute Monarchy", which very few countries actually have today. Said countries, as examples, are Saudi Arabia, Oman, and Eswatini (formerly known as Swaziland).
In such countries, the monarch has almost no opposition from their subjects, and their word is final. The only way to oppose such a leader, is to either kill or overthrow them, unless you can convince them that the country can reform into a constitutional monarchy. They are above the law.
Just a note before we move on. Most of the world today is composed of republics, not necessarily democracies, and the two do not have to be different from one another. My country, Israel, is a republic, not necessarily because it is democratic but because it has no monarchy. Great Britain, on the other hand, is not a republic, even though it is democratic like Israel is, with the reason being its monarchy.
The most ambiguous country in the world in terms of its regime is North Korea, or "The People's Democratic Republic of Korea". That's because, although NK is clearly a dictatorship, it is also the following: a communist dictatorship, a "monarchy" ruled by a single dynasty, and strangely of all, a "necrocracy."
As far as I know, North Korea today is the only country in the world where the previous, deceased leaders are still considered rulers of the country, even though they're dead. The country's founder, Kim Il-sung, is even considered "the Eternal Supreme Leader of the DPRK".
A Necrocracy is a paradox I believe we can all learn from. In philosophy, we use logic to get to the truth. However, in reality, not all truths are necessarily logical. The "Necrocratic Paradox" is simple: if the dead rule the country, then the actual leaders of said country are not their actual leaders. The head of state is essentially a corpse.
Kim Jong Un, the current leader, is the recognized leader of that country both outside and from within, but if your country is necrocratic, then the current Kim is, technically, not the "true eternal" leader, as that honor is preserved for his grandfather, who created the country. The current Kim, therefore, is both a leader and not an actual leader, if that makes sense.
It doesn't make sense, because a leader cannot be both a leader and not a leader. The original grandfather is no more, but legally he is the true ruler, so "true" that he is sacred, and just like with Jesus Christ across the world, the North Korean calendar begins with Il-sung's birth back in 1912.
The paradox in question, therefore, demonstrates that a leader can lead without necessarily being the "true" leader, no matter how much they are recognized in both respect and in the execution of their commands. It is also a paradox because there is a distinction between "regular truthfulness" and "true truthfulness,", as if the truth has at least two layers to itself.
As if there is more "true" than actual true, like the current Kim is just a leader while his grandpa is the "true" leader, which doesn't make sense at all. And yet, while not officially recognized, North Korea is probably the only country where at least the founding father continues to rule his country from the grave, alongside the alive, "actually true" leader, Kim Jong Un.
Does truth have, at times, more than one layer of "true" to it? Is there more truth to the equation, 1+1=2, or is such a belief too redundant to even be practical? A Necrocracy is just redundant, and therefore, illogical. Why would a country need to honor its dead to the point of giving them legitimacy to rule, when they cannot, technically, rule, given their situation? Why does a corpse need to rule alongside a living being, when only the latter can truly lead? (These aren't necessarily rhetorical questions. Feel free to comment on why).
That is, ladies and gentlemen, why illogical things can exist. They can exist because different people have different capacities for logic, and I'm not saying it to sound arrogant. The "bitter" truth is that there are people who are more logical than others, just as there are people who are less rational than others.
Thus, it would only be logical that less rational people would create more fallacies and mistakes than their more rational counterparts. I myself am very bad at mathematics, and thus I made a lot of mistakes when calculating equations back in school.
However, due to my better ability to express myself literarily, I became a philosopher in my quest for better understanding existence, and sharing my findings with you.
The premise, "what isn't logical can't exist" isn't true, because if I write 1+1=3, even if incorrect, it will exist at least where I have written it (like here, for example), and that is the very insight I wish to deliver to you.
Logic, while a great tool for better knowing about existence, is not always sufficient, because the world was conquered by a species whose members aren't all as rational in their decision making, and aren't as introspective, in the results of their efforts, regardless of field.
The increase of our rationality is our own choice.