Abstract:Inspired by Nuel Belnap's "How a computer should think," which gave rise to the four-valued logic FDE, we contemplate, in this article, how a computer might think if we add a fifth value for unknowable or cannot be known. We devise two new five-valued logics, UKN1 and UKN2, called the logics of the unknowable. These are different from the five-valued logic FDEe of the FDE-family. The main difference is in the number of designated truth values. While FDEe takes two designated values, UKN1 and UKN2 have three. The four-valued reducts of these logics are also different from FDE. This is due to the fact that instead of taking one of the non-designated values as neither true nor false, as in FDE, we have interpreted this as not known yet. This value although denoted by the same letter $n$, behaves differently from its namesake in FDE.
From: Sankha Basu [view email]
[v1]
Sun, 21 Jun 2026 12:59:21 UTC (13 KB)
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