information order: N below T and F, both below B · dimmed cube = not in C(S)
NS_KernelReentry · §0.1 and §0.10
Four values, one register closure
A register S is a subset of Belnap FOUR, with its own membership for N, T, F and B. The native solver computes the least fixed point of H(S) = S ∪ {B}, which is L = {B}. Closure is C(S) = S ∪ L.
Choose the members of S
S = {{sStr}}
L = lfp H = {B}
C(S) = {{cStr}}
C(C(S)) = C(S) · fixed: {{fixedStr}}
∅ → H(∅) = {B} → H({B}) = {B}. The iteration stops after one step.
Read paraconsistently, B = (1, 1) is a value held without trivialising: evidence for and against sit together, and nothing else follows from B alone. The fixed point is Inc(B) = B, and every value is carried to B by Inc.