How do I wrote floor() without boolean logic?

How do I write a floor function without using boolean logic?

You've got to start with some axioms. In computing int() can be considered an axiom because it relies on the hardware implementation. Doesn't need logic as such, you just dump the non-integral part.

In maths the axioms are usually considered to be logic and set theory, so if you want to reduce the problem down to the axioms but you don't want to use logic, well, that's not gonna happen.