Restricting to classical throws the held value away
Two truth-order adjunctions, ex falso c and ex quodlibet r, retract the four Belnap values onto the two-valued Boolean core. Choose a map and a value, then follow where it lands.
Layer of four: N, T, F, B. Layer of two: F, T. Dashed rings mark values the core has no name for.
RESTRICTION MAP
BELNAP VALUE
{{lineMap}}
{{lineRound}}
{{lineCollide}}
c : N→F T→T F→F B→F
r : N→T T→T F→F B→T
The adjoints disagree on B and neither returns it. No map on {F, T} can express B, so the collapse is exactly lossy (Theorem 4.4).