Beyond a defensible answer.

An answer can be defensible under one interpretation and inadmissible under another. The relevant object is therefore not an isolated proposition, but the relation between a proposition, its evidential context, and the interpretive commitments under which that relation is evaluated.

Assessment design sits inside this distinction. A passage does not merely contain facts; it distributes commitments across scope, modality, reference, and qualification. A response may preserve the vocabulary of those commitments while altering their logical force. Conversely, a response may depart substantially from the wording while preserving the relation that matters.

Neither lexical proximity nor explanatory fluency is sufficient to resolve the distinction. The evaluation problem is relational: whether an interpretation is licensed by the relevant evidence without importing an unacknowledged premise, relaxing a material restriction, or substituting a weaker conclusion for the requested one.

$$𝒜=\bigcap _{i\in I}{𝒞}_i$$

Correctness is a judgment about an answer.
Admissibility is a judgment about the conditions of that judgment.

Interpretation-relative closure +

Closure is meaningful only relative to a specified inferential regime. Treating an evidential context as closed under arbitrary background knowledge can enlarge the defensible conclusion set beyond the intended task; treating it as closed under literal restatement can exclude legitimate abstraction. The resulting boundary is neither purely syntactic nor reducible to a single scalar similarity measure.

This creates a distinction between the extension of a response under a selected reading and its stability across the readings the task reasonably permits. Apparent agreement at the extension level can coexist with disagreement about the admissible interpretive domain.