BF-algebra

In mathematics, BF algebras are a class of algebraic structures arising out of a symmetric "Yin Yang" concept for Bipolar Fuzzy logic, the name was introduced by Andrzej Walendziak in 2007. The name covers discrete versions, but a canonical example arises in the BF space [-1,0]x[0,1] of pairs of (false-ness, truth-ness).
Definition.
A BF-algebra is a non-empty subset formula_1 with a constant formula_2 and a binary operation formula_3 satisfying the following:
Example.
Let formula_7 be the set of integers and 'formula_8' be the binary operation 'subtraction'. Then the algebraic structure formula_9 obeys the following properties: