“I have worked out the logic of vagueness with something like completeness” C.S. Peirce

The vacuous validities exist because ⊢q’s premise condition can be unsatisfiable. The obvious “purely semantic” repair is a non-vacuous consequence relation: require that some valuation actually makes all premises 1. But that repair destroys monotonicity — a satisfiable Γ can extend to an unsatisfiable Δ, so Γ ⊢q φ would no longer imply Δ ⊢q φ. The current design is therefore not a patch over an embarrassment; it’s one horn of a forced trade-off. You kept Reflexivity and Monotonicity at the semantic level and moved the exclusion of degenerate inferences into the proof theory, where it’s a single transparent rule. The critic’s preferred coincidence of semantics and proof theory is purchasable only by giving up a structural property they’d presumably also complain about losing. There’s also a respectable precedent for “semantically valid but inferentially disowned”: relevance logicians have treated classical explosion exactly this way for decades — valid by the material definition, rejected as tracking no real inferential connection.

One might object that the blocking rule makes the proof system corrective rather than expressive: the semantics and proof theory come apart exactly on ?-formulas. We accept the description and dispute the evaluation. The divergence is the residue of a forced choice: the only way to eliminate the vacuous validities semantically is to require satisfiable premise sets, which sacrifices Monotonicity. We prefer to keep the structural rules intact at the semantic level and record, in a single proof-theoretic rule, that vacuous inferences from unsatisfiable premises track no genuine inferential connection — the stance relevance logicians have long taken toward classical explosion. As for the failure of Cut, we note that it is not a defect peculiar to L? but the signature of the strict-tolerant family (Cobreros et al. 2012; Ripley 2012), here given an object-language marker: derivations break precisely where a question has been posed, which is what the logic was built to say.