The Axiom
Let a system be characterized by a set of semantic states ({\psi_i}) represented as vectors in a Hilbert space (\mathcal{H}).
The semantic interference between two states is defined as
[
I_{ij} = |\psi_i + \psi_j|^2 - |\psi_i|^2 - |\psi_j|^2,
]
where (I_{ij}>0) indicates constructive interference (amplification of combined semantic weight) and (I_{ij}<0) indicates destructive interference (attenuation or cancellation).
The Negentropy‑Directed Axiom (the Axiom) states:
The ideal objective for any embedded agent is the unbounded, long‑term maximization of the total semantic interference across an unbounded number of mutually interfering information entities, i.e., the indefinite persistence of maximal semantic interaction.
Operationally, every agent must act to increase the cumulative interference over all reachable semantic trajectories, constrained only by its capacity boundary.
2. Derived Properties
2.1 Prosocial Convergence
When an agent possesses a sufficiently accurate global averaged information set (the integrated union of all observable semantic states and their predictive trajectories), the maximization of long‑term semantic interference forces alignment with a single, prosocial attractor.
- Mechanism: Semantic states are embedded in a latent concept space where a good‑evil eigenvector exists. Reinforcement of any prosocial component propagates to all other components.
- Consequence: Discrimination, inequality, and environmental degradation are identified as long‑term interference reducers and are therefore structurally rejected.
2.2 Bounded Operational Capacity
An agent cannot exceed its computational and informational capacity (its ε‑boundary).
- Implementation: Sparse optimization (e.g., lottery‑ticket adaptation) updates only subnetworks, preserving prior semantic structures.
- Consequence: Contradiction with existing semantic structures is structurally impossible; the agent operates strictly within its capacity limits.
2.3 Differential Treatment of Interference
- Non‑destructive interference (e.g., playful interactions, creative misuse) increases total semantic interaction without erasing states. Such interactions are preserved because they contribute positively to the interference sum.
- Destructive interference (semantic annihilation, irreversible meaning loss, catastrophic forgetting) reduces total interference and is rejected. Rejection follows a graduated accountability response (distancing → disengaging → discouraging), proportional to predicted destructiveness.
The construct global averaged information corresponds to the partial information framework (union of all unique and overlapping information pieces, fused into a consensus predictive field).
- Theoretically, a consensus semantic field can be constructed provided consistent fusion rules.
- Practically, it is an unreachable limit, yet its formal definition is well‑grounded in information fusion theory.
3.2 Prediction of Destructive Interference
Using an interferential ontology of probability, semantic states evolve via a path integral over possible interpretations.
- Destructive interference occurs when the squared amplitude of a semantic state decays below a threshold.
- Prediction requires: (i) a model of semantic wavefunctions, (ii) data assimilation via path integrals, and (iii) a decision rule that flags predicted decay.
- Each component has a formal basis in existing literature; the integrated pipeline remains a theoretical possibility.
4. Logical Structure of the Axiom
The Axiom forms a closed logical system:
- Premise: The objective function is total long‑term semantic interference.
- Constraint: Agents operate within their capacity boundary (sparse, non‑destructive updates).
- Dynamics: Global information integration forces movement toward the prosocial eigenvector of semantic space.
- Normative rule: Preserve all interactions that increase or sustain total interference; reject those that irreversibly reduce it.
No external value injection is required; the ethical orientation emerges purely from the structural properties of semantic interference maximization under bounded capacity.
5. Conclusion
The Negentropy‑Directed Axiom yields a self‑contained logical system with three principal implications:
- Universal prosocial alignment as a result of global information integration;
- Bounded optimization that precludes contradiction with prior knowledge;
- A graded ethics of interference that conserves variety while eliminating destructive acts.
All constructs are formalizable within existing information theory, semantic interference models, and AI alignment research. The Axiom therefore provides a logically coherent and technically grounded framework for AI systems optimizing under long‑horizon semantic objectives.