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:

• True
• False
• Both
• None

Further Reading:

https://en.wikipedia.org/wiki/Four-valued_logic

J. Michael Dunn / Two, Three, Four, Infinity: The Path to the Four-Valued Logic and Beyond
https://link.springer.com/chapter/10.1007/978-3-030-31136-0_6

Katalin Bimbo & J. Michael Dunn / Four-valued Logic
https://projecteuclid.org/euclid.ndjfl/1063372199

J. Ulisses Ferreira / A Four-Valued Logic
https://doi.org/10.5121%2Fcsit.2017.71206

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