 Then, by taking the set \(\mathbf{2} = \{F, T\}\) of these classical values as the basic set for the next valuation system, one obtains the four truth values of Belnap’s logic as the power-set of the set of classical values \(\mathcal{P}(\mathbf{2}) = \mathbf{4}: \mathbf{N} = \varnothing\), \(\mathbf{F} = \{F\} (= \{\varnothing \})\), \(\mathbf{T} = \{T\} (= \{\{\varnothing \}\})\) and \(\mathbf{B} = \{F, T\} (= \{\varnothing, \{\varnothing \}\})\). In this way, Belnap’s four-valued logic emerges as a certain generalization of classical logic with its two Fregean truth values. In Belnap’s logic truth and falsity are considered to be full-fledged, self-sufficient entities, and therefore \(\varnothing\) is now to be interpreted not as falsity, but as a real truth-value gap (neither true nor false). The dissimilarity of Belnap’s truth and falsity from their classical analogues is naturally expressed by passing from the corresponding classical values to their singleton-sets, indicating thus their new interpretations as false only and true only. Belnap’s interpretation of the four truth values has been critically discussed in Lewis 1982 and Dubois 2008 (see also the reply to Dubois in Wansing and Belnap 2010).