A more mathematically rigorous implementation might consider the incompleteness theorems and actually need a third option between true and false (i.e. undecidab

A more mathematically rigorous implementation might consider the incompleteness theorems and actually need a third option between true and false (i.e. undecidable). There are non-Boolean algebras out there, such as Kleene's. So us seeing Boolean algebra as the king is mostly a historic outgrowth, not a fundamental truth.