Logic is not as absolute as we would like it to be. For example, linear logic breaks down normal logic into a realm of substructurality. There seems to be several ways to consider expanding classical two-valued logic to four values.
Let this post be a placeholder for considering expansion of classical two-valued logic to four values. For example, one might have:
J. Michael Dunn / Two, Three, Four, Infinity: The Path to the Four-Valued Logic and Beyond
Katalin Bimbo & J. Michael Dunn / Four-valued Logic
J. Ulisses Ferreira / A Four-Valued Logic