Usually, the extension of classical logic to a three-level valued logic results in a complicated calculus, with side-conditions on the rules of logic in order to ensure consistency. One reason for the necessity of side-conditions is the presence of nonmonotonic operators. Another reason is the choice of consequence relation. Side-conditions severely violate the symmetry of the logic. By limiting the extension to monotonic cases and by choosing an appropriate consequence relation, a simple calculus for three-valued logic arises. The logic has strong correspondences to ordinary classical logic and, in particular, the symmetry of the Genzen sequent calculus (LK) is preserved, leading to a simple proof for cut elimination.
