Append-Only Answerability Monotonicity

Abstract

Appending records preserves every target answerable from the old history.

Theorem 1.1 (Answerable historical targets persist after appending records).

$$\forall Gamma\in Type,Bn\in Type,Bnext\in Type,Y\in Type,Ln\in Gamma\to Bn,Lnext\in Gamma\to Bnext,pn\in Bnext\to Bn,Ln=\mathrm{compose}(pn,Lnext)\Rightarrow \mathrm{AnswerableTargets}(Ln,Y)\subseteq \mathrm{AnswerableTargets}(Lnext,Y)$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/History/AppendOnlyAnswerabilityMonotonicity.append_only_answerability_monotone (✓ std3). ∎

Source. Repository-derived.

Commentary.

The old and new logs are concepts on the same history-index carrier. Appending records supplies a projection from the new log values to the old values, and the displayed equation states that the old log is recovered by this projection.

AnswerableTargets is the canonical set of target concepts whose readouts factor through a history concept. Composing the append projection with each old recovery map gives the required new-log recovery map.

References

• Truth anchor: D5/S3/ConceptDynamics/History/AppendOnlyAnswerabilityMonotonicity.append_only_answerability_monotone
• Dependency: D5/S3/ConceptDynamics/Answering/AnswerableTargetMonotonicity