All numbers that can be noted in the decimal system can also be noted in the binary system.
The binary system has boolean operators. Some basic boolean operators are: and $\land$, or $\lor$ and not $\lnot$. I don't know any corresponding operators in the decimal system.
As far as I've learnt about boolean operations, they are discrete. But, you can represent real numbers in the binary system:
$\pi = 3.1415926535..._{10} = 11.0010010000111111..._2$
and so you can apply boolean operators on real numbers. Which makes them continous.
So I would like to learn what happens, if boolean operators are used in a continous way but not discrete. I am specially interested in the xor operator, which has fascinating properties and is defined as:
$A \oplus B = (A \lor B) \land (\lnot A \lor \lnot B)$
Finally, I would like to examine things like: $\pi \oplus \sqrt{2}$
Question: Can you give me references to literature about continuous applications of boolean logic, or
can you show me meaningful keywords of the more general matter?
For instance, Boolean algebra is a special case of a De Morgan algebra. Or it could be in the context of modular arighmetic. But I don't know if it makes sense to search there. I didn't found suitable papers by searching with "continuous applications of boolean operators" or else. There is also "continuous logic" but this is something different.