A pair of sets of points in R^n are called linearly separable if there exists a Hyperplane which separates them (that is one set is on one side, and the other is in the other side of the hyperplane).

A function from R^n to {0,1} is called linearly separable, if its Level sets $f^{-1}(1)$ and $f^{-1}(0)$ are linearly separable. Such a function is also called a linear threshold function

A particular class of these are Threshold Boolean function

Connections to Assumability etc here

https://en.wikipedia.org/wiki/Linear_separability

A Consistent learner for linear threshold functions

See here. Basically a linear program to check if a set of points are linearly separable