1 Semantics
Truth values are \(T\) and \(F\); the third symbol \(Z\) is a mark for an unverified input, not a truth value.
For a classical connective \(f\), its ZTL lift returns \(T\) iff \(f\) is forced to \(T\) under every classical reading of \(Z\); otherwise \(F\). Truth is never granted on credit.
All six connectives are lifts of their classical cores; no table is postulated.
The design anchor cells hold: \(\neg Z=F\), \(\neg \neg Z=T\), \(Z\leftrightarrow Z=F\), \(Z\oplus T=F\), etc.
Every compound formula is classical under every valuation: \(Z\) lives only on atoms.