How can I control carts with logic? Can I create a splitter for them? Give all the examples of using logic with this.

There are some docs in the wiki:

https://gitlab.com/aerosuidae/logicarts/wikis/circuit-network
https://gitlab.com/aerosuidae/logicarts/wikis/stickers

I guess you're thinking of something like a belt splitter, but for carts. With the current feature set of the mod you'd probably have to build something like a flip-flop circuit to alternate L and R signals. I've never tried this, so it would be great to see the result if you get it working!

I was able to realize this. But it would be great to do it without a gate, but I do not know how to do it.
https://radikal.ru/video/MBI4OWIK6af

And I still don't understand what the "Depart stop" will do.

That is thanks to your links, I now know how to make a splitter without a gate, but the splitter with a gate turns out to be the most compact, its dimensions are 3x4.

My scheme is based on the algebraic logic . When a cart passes through a path with a permanent combinator, the system receives the indicated sign, if it is in the cart, then this sign is preserved by binding the input and output of the arithmetic combinator, then it is followed by a conjunction with 1. This sign at the cart should always be = 1, otherwise the circuit will not work correctly. 1∧1=1, the gate receives the sign = 1 and closes. The next combinator sends a new one, which is stored in the arithmetic combinator, where there is already such a unit and the sign becomes equal to 2. 2 this is ¬1 (not 1), therefore 1∧¬1=1∧0 = 0, the gate gets 0 and opens, the obstacle disappears.

I think I was able to make a splitter for carts without gates, size 3x3.

https://radikal.ru/video/ItR58RNV9jj

If we add another comparison combinator to eliminate the problem with a fixed value of the attribute always equal to 1, then the size of the scheme will increase and become equal to 3x4 or 3x5.
Perhaps it is worth making all carts have a common attribute = 1 that they could send to the logical network?

And do something so that in order to organize loading and unloading areas there was no need to use combinators.
https://c.radikal.ru/c07/1906/3a/49b8f1e7156b.jpg