based on an earlier version of the Wolfram Language.
Mathematica represents Boolean expressions in symbolic form, so they can not only be evaluated, but also be symbolically manipulated and transformed. Incorporating state-of-the-art quantifier elimination, satisfiability, and equational logic theorem proving, Mathematica provides a powerful framework for investigations based on Boolean algebra.
Boole — convert symbolic truth values to 0 and 1
BooleanFunction — general Boolean function
FullSimplify — simplify logic expressions and prove theorems