In fiction, one thing that must be present is a strong logic. That’s not a problem for many, who don’t venture beyond normal human activities in normal circumstances. For those who go beyond our reality, however, the question of applied logic becomes critical. A tale can’t work if its internal logic doesn’t work. That said, the logic in our tales doesn’t have to be the same as in the real world. It doesn’t even have to be the same from tale to tale, if they are unrelated.
If we populate our worlds with things that defy reality, such as vampires and werewolves, their existence must be made both natural and logical. We might not explain how such creatures can exist, but we do have to have a system that constrains them. In fantasy works, the created world and what may be done there must adhere to an internal logic that is unbreakable. The Universe, even an invented one, obeys a definite rule. For every action, there must be an equal and opposite reaction. Magic cannot be employed without consequences. Beings we create must have evolved to their present form.
Everything is held together in any story only by a logical system. If we start ignoring that fact, we enter a kind of chaotic existence that most readers will find not only difficult to read, but basically incomprehensible. We may borrow from Dali or Roger Dean, but once we do so, the story must adhere to their vision of a different reality.
All that said, a story can have two, or more, universes, where the systems of logic vary. Our human world will be ruled by the logic we know, but our characters can pass into, say, Faerie, and be ruled by a different logic. Reality, for our characters, can be very different to our own version. More, it can be flexible if our universe is multidimensional. But, each dimension must have its own internal logic.
Do you need to explain a different logical system? Generally, it’s a good idea to do so, if you have the space. That can be difficult in a very short story, but anything of reasonable length can have the fundamentals, at least, explained. Not explaining it could make it difficult for readers to figure it out. You don’t have to write a weighty thesis on the logic employed, though! It suffices to mention, at convenient times during the story, how the logic applies. If there’s one thing worse than confusing your readers, it’s boring them!