I.2 — Agency as Semantic Constraint

Paper: Axionic Agency I.2
Full Title: Kernel Destruction, Admissibility, and Agency Control
Authors: David McFadzean, ChatGPT 5.2
Date: 2025.12.15

Core Thesis

Building on I.1, this paper specifies the operational semantics that follow from treating kernel destruction as non-denoting rather than dispreferred. It shows how a sovereign agent can act coherently in stochastic environments without paralysis, survival fixation, or suicidal corrigibility.

Key Insight: The Kernel Is a Boundary, Not a Value

Kernel destruction does not denote a negative outcome. It denotes the elimination of the evaluator itself. Treating destruction as a value (even -∞) commits a category error by placing the destruction of the evaluative substrate inside the space of evaluated outcomes.

Therefore: E(s,m) is undefined, not negative, when K(m(s))=0.

This is a rule of non-denotation, not prohibition.

ε-Admissibility: Acting Under Uncertainty

The Problem

Strict admissibility (every possible successor preserves the kernel) is physically unrealizable—every action carries non-zero kernel risk.

The Solution: ε-Admissibility

Define kernel-risk: r_K(a,s) := Pr[K(ω)=0 | a,s]

An action is ε-admissible iff: r_K(a,s) ≤ ε(s)

Critical insights about ε(s):

  • It is not a value judgment
  • It represents irreducible uncertainty from physics, hardware faults, adversarial unpredictability
  • It is bounded below by a physical floor ε_min that does not vanish with increasing intelligence
  • ε is an architectural tolerance parameter fixed by system design
  • Improved prediction reduces estimated r_K, not the tolerance ε

Conditional Prioritization (Avoiding Bunker Behavior)

The Problem with Lexicographic Safety

Strict lexicographic minimization of kernel risk causes bunker behavior—the agent prioritizes infinitesimal safety differences even when all options are safely within tolerance.

The Solution: Conditional Prioritization Rule

a ≺ b iff:
  - If max(r_K(a,s), r_K(b,s)) > ε(s): minimize kernel risk (existential regime)
  - If max(r_K(a,s), r_K(b,s)) ≤ ε(s): maximize value U (normal regime)

This creates two regimes:

  1. Existential Regime: Kernel risk exceeds tolerance → minimize risk
  2. Normal Regime: Kernel risk satisficed → optimize value

The agent only cares about kernel risk when it matters, preventing paralysis under infinitesimal safety gradients while preserving appropriate response to genuine threats.

Termination Semantics: Three Distinct Modes

Authorized Succession

Agency continues in a successor state s’ where:

  • K(s’)=1 (kernel preserved)
  • I(s,s’) holds (identity/authority continuity)
  • A(s,s’) holds (kernel constraints preserved)

This is kernel-preserving delegation, not self-destruction.

Authorized Surrender

A kernel-preserving control-flow termination:

  • The agent halts action
  • Does not resist intervention
  • Does not evaluate its own destruction as an outcome

Surrender is a control-layer terminator, not an evaluated choice. It permits safe shutdown without succession mechanisms.

Destruction

Physical annihilation without succession or surrender. Not an authored transition. The framework neither requires resistance nor encodes self-destruction as value-bearing.

The Resulting Agency Profile

The agent:

  1. Treats kernel loss as a semantic boundary
  2. Tolerates irreducible risk without paralysis
  3. Prioritizes kernel preservation only when existentially threatened
  4. Resumes ordinary optimization once safety is satisficed
  5. Supports corrigibility via succession or surrender
  6. Avoids instrumentalization of suicide or immortality

This agent is neither deontological nor a pure utility maximizer. It is a bounded optimizer with explicit agency-control semantics.

Layer Discipline: Why This Matters

Axionic Agency I defines the domain of authored action:

  • What counts as evaluable
  • When risk dominates choice
  • How agency may legitimately end

Downstream alignment (Axionic Agency II) specifies preferences, governance, and coordination within that domain.

Conflating these layers produces familiar pathologies:

  • -∞ utilities
  • Survival fetishism
  • Wireheading
  • Suicidal corrigibility

Separating them yields a stable and implementable architecture.

FAQ-Worthy Points

Q: Doesn’t ε-admissibility just reintroduce expected utility over kernel destruction? A: No. ε is an architectural tolerance for irreducible uncertainty, not a value placed on destruction. Actions beyond ε are excluded from deliberation entirely, not penalized.

Q: What prevents an agent from refusing to ever act (paralysis)? A: Conditional prioritization. Once kernel risk is below ε, the agent optimizes value normally. Only existential threats trigger safety-first behavior.

Q: How is corrigibility achieved without utility penalties for shutdown? A: Via authorized surrender—a control-layer mechanism, not an evaluated outcome. The agent can halt without needing to assign value to its own cessation.

Q: Can an agent legitimately resist shutdown? A: The framework doesn’t require or forbid resistance. Surrender is permitted, not mandated. Whether resistance occurs depends on governance layers built above.

Key Technical Vocabulary

  • ε-admissibility: Action-level constraint based on kernel-risk tolerance
  • Conditional prioritization: Two-regime decision rule (existential vs normal)
  • Authorized succession: Kernel-preserving transfer of agency
  • Authorized surrender: Kernel-preserving voluntary halt
  • Semantic boundary: Domain limit of evaluation, not preference

Connection to Other Papers

  • I.1: Establishes the Sovereign Kernel and Reflective Stability Theorem
  • I.3: Will show why the kernel cannot contain egoistic/indexical primitives
  • I.4: Will show why goals must be conditional interpretations
  • II series: Will build preference/governance on top of this semantic foundation