Other space ability users include: Rimbaud, Poe, Louisa, Nikolai, Kunikida, Akutagawa, and Tanizaki. Some more so than others (Lucy, Poe, Tanizaki, Akutagawa). For some it only loosely applies or needs some justification/explanation for it to apply (Kunikida, Louisa). The best examples by FAR are Lucy and Poe. 

Time abilities: 

“Time related abilities” refer to abilities that break normal laws of time. I.e. by slowing it down/stopping it, repeating it, speeding it up, etc. Some ability users have abilities that deal with both space and time (again, prime example being Lucy ) usually by having an ability that creates or inhabits its own space with its own time.

Other time ability users include: Louisa, the Meursault cat-girl, Oda, and POSSIBLY Teruko depending on how you look at it. 

Matter abilities: 

“Matter related abilities” refer to a LOT of abilities in bsd. Any ability that allows someone to shapeshift, create something, destroy something, or change something is matter related. A lot of these abilities likely even go against the law of conservational mass; however, they might not if given the correct explanation. 

For example: Akutagawa. You could argue the matter is not being created with his ability(though it's unlikely) and that the extensions from his coat are still the same mass as the part of the coat it’s from. This could be achieved by Rashomon becoming less dense and more fluid in relation of how far away it’s stretched from Akutagawa’s coat. And because his ability is said to be able to cut through space itself, that would also count as a space related ability. 

And for an example of an ability that most definitely breaks the law of conservation of mass, is Thou Shalt Not Die. Sense her ability can heal things like lost limbs, blood loss (S1 Tanizaki, S4 Kenji), etc., matter must be created for her ability to work. You could not give an explanation like Akutagawa’s, because her ability results in injuries being fully healed and that part of the body remaining functional.  

Other matter ability users include: Atsushi, Kyouka, Kouyou, Fyodor, Pushkin, Ivan, Shibusawa, Natsume, Mushitaro, Tetcho, Melville, Jouno, Steinbeck, Mori, Lovecraft, and Teruko (again, depending on how you look at it). 

Teruko’s ability: 

Teruko’s ability could be argued to either be a matter ability, or a matter AND time ability. On one hand, it could be taking the actual previous and future ages of the person she’s using her ability on (kind of like Mirai from TBHK iirc). In this case, it would be a time and matter related ability. On the other hand, it could just be changing the person’s physical appearance and anatomy based on factors unrelated to the actual “keyframes” past or future of that person's life. In this case, it would only be a matter related ability. 

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How Abilities Work:

Abilities are, as previously stated, directly related to the fourth dimension. That's what gives them the ability to manipulate 4th Dimensional and 3rd Dimensional elements like time, space, and matter.

Each ability is it's own very niche gateway to interacting with and breaking basic structures and laws of the third and/or fourth dimension.

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Dazai and Gozen:

Gozen:

Quick circle back to Fyodor: 

What confused me for so long about his plan is why is he wanting to manually kill off/start war against all ability users instead of using the page(<- probably dysfunctional) to get rid of abilities? If he truly wants to purge the world of “sin” (abilities) then why kill the people who didn’t even choose to have an ability (/who didn’t choose to be exploited by the government)? Why not get rid of the problem itself: abilities?  

And a possibility is that ability users would die without their abilities. If he simply writes abilities themselves out of existence and ends up getting all ability users killed, then to him it would've essentially been like killing a ton of innocent people. He's antagonizing them for his own sake as well as for his plan to group everyone together through a common enemy/fear.

And then there’s how the deaths from Gozen’s sword are portrayed. 

Which circles to “why the bubbles?” For one, it's a way for the death to be more easily communicated to the reader. Simply drawing a character just lying in a puddle of their own blood can be easily misinterpreted as them simply being heavily injured but not dead yet. The bubbles are a stylistic choice to show that there’s a difference in the nature of deaths caused by Gozen compared to any other way of dying. 

The “death” that Gozen gives to whoever he kills is not essentially just death itself. The heart doesn’t stop, the body doesn’t die, and the brain is still intact up until it gets turned into bubbles. 

Gozen severs the connection between the ability user and their ability. And given that: 

Gozen is a fourth dimensional being 

Fukuchi’s ability  

Fyodor’s objective to kill ability users + his control over Gozen’s actions(and therefore how Gozen interacts with the 4th dimension) 

Gozen is perfectly capable of severing the ability-ability user connection. With access to the fourth dimension, the strength (Fukuchi’s ability) to cut that connection, and the will and instructions (Fyodor) to do it, it could be possible that that’s how Gozen is killing off ability users. 

(BSD Chapter 115, ~ Page 30)

Dazai:

Given how abilities work, I propose that Dazai's ability can be summed up as being like an enzyme inhibitor but for abilities.

And Gozen's killing mechanism and Dazai's ability are really fucking similar. Gozen permanently severs the ability, whereas Dazai temporarily inhibits the ability.

However one piece of evidence I can provide is that Dazai's ability relies on him DIRECTLY touching the ability user or the physical mass of the ability. His ability places a temporary blocker to stop the connection between the ability user and their ability, which requires that either the physical manifestation of the ability or the ability user's body is touched so that the blocker can actually have an affect and therefore nullify the ability. And this is why Dazai's ability does no harm to the ability user, but Gozen's does.

Dazai's ability never permanently harms or changes the connection between an ability and ability user. Gozen's, however, does.

And this whole theory arguably makes Fyozai even gayer. What do you mean that you ensured that the killing mechanism of the divine being you smushed together is just an amplified version of your ex's ability?? gayass.