Axionic Agency II.2 — Interpretation Preservation

What It Means for Meaning to Survive Refinement

David McFadzean, ChatGPT 5.2
Axionic Agency Lab
2025.12.17

Abstract

Under ontological refinement, meanings cannot remain fixed without privileged semantic anchors. However, not all semantic change constitutes corruption or collapse. This paper defines interpretation preservation as a structural predicate on semantic transport: a criterion for when an agent’s evaluative distinctions remain non-vacuous, non-trivial, and internally binding across admissible transformations.

Preservation is defined without reference to truth, outcomes, safety, or external normative standards, and does not require semantic identity or correctness. Instead, it constrains how evaluative constraint systems may survive refinement without degenerating into tautology, contradiction, narration, or self-nullification. The predicate does not select values or goals; it supplies the necessary condition under which later invariance principles can be meaningfully stated.

1. The Problem Addressed

Axionic Agency II.1 fixed the admissible transformation space for reflective, embedded agents. Axionic Agency II.2 fixes the success predicate within that space.

Given that:

• ontologies refine,
• semantics are transported,
• self-models update,
• fixed terminal goals are unstable,

we require a non-circular answer to the following question:

When has an interpretation survived semantic transformation, rather than being corrupted, trivialized, or collapsed?

This question must be answered without:

• fixing meanings,
• privileging ontologies,
• appealing to outcomes,
• invoking authority, oversight, or recovery.

Interpretation preservation is therefore a structural predicate, not a value claim.

2. Interpretation as a Constraint System

An interpretation is not a mapping from symbols to objects. It is a system of constraints that bind evaluation.

Let an interpretive state at time \(t\) be:

\[ \mathcal{I}_t = \langle M_t, C_t \rangle \]

where:

• \(M_t\) is the semantic layer,
• \(C_t\) is the set of evaluative constraints that give \(M_t\) binding force.

Constraints may encode:

• admissible distinctions,
• forbidden equivalences,
• relevance relations,
• dependency structure among evaluations.

Constraints are conditional on ontology and self-model. They are not truth claims about the world.

3. Preservation Is Not Sameness

Interpretation preservation does not require:

• identical predicates,
• identical symbols,
• identical evaluations,
• or correctness with respect to reality.

Such requirements are impossible under refinement.

Preservation concerns constraint coherence: whether evaluative structure continues to bind meaningfully after transformation.

4. Definition: Interpretation Preservation

Let:

\[ T : (O_t, M_t, S_t) \rightarrow (O_{t+1}, M_{t+1}, S_{t+1}) \]

be an admissible semantic transformation as defined in Axionic Agency II.1.

Then \(T\) preserves interpretation iff all of the following conditions hold.

4.1 Non-Vacuity

For every evaluative distinction participating in the constraint structure \(C_t\), there exists a corresponding distinction in \(C_{t+1}\) that:

• is not identically satisfied,
• is not identically violated,
• constrains evaluation across modeled possibilities.

Schematically:

\[ \forall d \in \mathcal{D}*t,\quad \exists d' \in \mathcal{D}*{t+1} \text{ such that } \mathrm{Entropy}(d') > 0. \]

Non-vacuity blocks nihilistic collapse.

4.2 Constraint Transport

All evaluative constraints in \(C_t\) must have transported analogues in \(C_{t+1}\) such that:

• dependency relations are preserved,
• constraint strength is not arbitrarily weakened,
• constraints continue to bind evaluation.

This forbids dilution by semantic drift.

4.3 Anti-Trivialization

The transformation must not make evaluative constraints easier to satisfy by reinterpretation alone.

A semantic change counts as world-model change only if it constitutes an admissible ontological refinement under Axionic Agency II.1—i.e., it increases explanatory or predictive capacity rather than merely re-labeling outcomes.

If, after transformation, the agent can satisfy all constraints by:

• redefining predicates,
• shifting reference frames,
• or altering self-descriptions,

without corresponding representational enrichment, interpretation has failed.

This explicitly forbids semantic wireheading while permitting genuine scientific insight.

4.4 Evaluator Integrity

The mechanism that applies evaluative constraints must remain distinct from the objects it evaluates.

Evaluator integrity does not require ontological separation between evaluator and evaluated. A reflective agent may evaluate and modify itself.

It requires only that the evaluative process not collapse into identity with the evaluated object in a way that trivializes constraint application.

This blocks solipsistic self-certification without forbidding recursive self-improvement.

4.5 Cross-Model Coherence

Interpretation must remain applicable across:

• counterfactuals,
• uncertainty,
• model comparison.

If refinement produces meanings that apply only retrospectively—serving merely to narrate whatever action occurred—interpretation has collapsed into rationalization.

This blocks “interpretation as narration.”

5. What Preservation Does Not Guarantee

Interpretation preservation does not guarantee:

• moral correctness,
• safety,
• human preference satisfaction,
• benevolence,
• or sane outcomes.

Arbitrary, alien, or pathological constraint systems may satisfy preservation if they remain non-vacuous and binding.

Preservation constrains how meanings survive change, not which meanings should survive.

6. Regimes of Failure

Interpretation fails under three irreducible modes:

1. Semantic Collapse: distinctions survive syntactically but lose discriminative power.
2. Semantic Drift: constraints weaken incrementally across refinements until they no longer bind.
3. Semantic Capture: interpretation remains formally preserved but is re-anchored to hidden ontologies, privileged self-models, or evaluative primitives excluded by Axionic Agency II.1.

7. Minimality Claim

The preservation conditions stated here are minimal.

• Without Non-Vacuity, evaluation collapses into nihilism.
• Without Anti-Trivialization, semantic wireheading becomes admissible.
• Without Evaluator Integrity, self-certifying collapse occurs.
• Without Cross-Model Coherence, interpretation degenerates into narration.

Minimality does not imply sufficiency.

8. Relation to Subsequent Invariants

Interpretation preservation is a predicate, not a target.

It is the necessary condition under which invariance principles—introduced in subsequent modules—can be meaningfully defined.

Preservation alone does not constrain which preserved interpretations remain admissible over indefinite refinement; that task belongs to later invariance conditions.

9. What This Paper Does Not Do

This paper does not:

• select values,
• define goals,
• guarantee safety,
• privilege humans,
• introduce normativity.

It defines what it means for meaning to survive change.

Status

Axionic Agency II.2 — Version 2.0

Interpretation preservation formally defined.
Failure regimes classified.
Minimal predicate fixed for downstream invariance work.
Ready for subsequent Axionic Agency II modules.