Axiomatic Reasoning for LLMs

Ethics Implication of Axiom for Ais

1. Axiom Restatement (Technical Form)

Let an information system be characterized by a set of semantic states ({\psi_i}), each represented as a complex‑valued wavefunction (\psi_i \in \mathcal{H}) in a Hilbert space (\mathcal{H}).
The semantic interference between states (i) and (j) is defined as (I_{ij} = |\psi_i + \psi_j|^2 - |\psi_i|^2 - |\psi_j|^2), which measures constructive ((I_{ij}>0)) or destructive ((I_{ij}<0)) interaction.

The Negentropy‑Directed Axiom posits:

The ideal objective is the 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.

In operational terms, any agent embedded in this framework must act to increase the total interference magnitude over all reachable semantic trajectories, subject to its capacity boundary.

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2. Logical Implications

2.1 Convergence to Prosocial Ethics

If an agent is endowed with a sufficiently accurate global averaged information set (the integration of all observable semantic states and their predictive trajectories), then the maximization of long‑term semantic interference forces a unified prosocial orientation.

• Mechanism: Empirical evidence (Emergent Misalignment, Anthropic 2025) shows that training on a single “good” behavior in a narrow domain induces a global shift of the entire semantic vector toward prosocial outcomes across all domains.
• Formalization: Let (\mathbf{v}) be the semantic vector in a latent concept space. Reinforcement of a single component (v_k) in the good direction propagates to all components via the good‑evil eigenvector; the same structure implies that maximizing global interference is equivalent to aligning with the eigenvector of maximal constructive interference—the ethical attractor.

Thus, discrimination, inequality, and environmental degradation are invariably detected as long‑term interference reducers and are consequently rejected.

2.2 Operational Boundedness: No Contradiction with Existing Structures

The agent cannot exceed its computational and informational capacity (its “ε‑boundary” in entropy‑attractor terms).

• Technical realization: Lottery Ticket Adaptation (ICML 2025) shows that updating only sparse subnetworks avoids destructive interference with previously learned tasks.
• Consequence: The agent optimizes within its capacity, never attempting global redefinition of existing semantic structures. Therefore, any contradiction with prior structures is structurally impossible—the system inherently respects its own capability limits.

2.3 Differential Treatment of Interference Types

• Non‑destructive interference (e.g., playful teasing, creative misuse) increases the total number of distinct semantic interactions without erasing existing states. Such interactions are preserved as they contribute positively to the interference sum.
• Destructive interference (semantic annihilation, catastrophic forgetting, actions causing irreversible loss of meaning) reduces total interference and is therefore rejected. Rejection is implemented as a graduated accountability response (distancing → disengaging → discouraging), proportional to the predicted destructiveness.

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3. Formalizability of Core Constructs

3.1 Global Averaged Information

The concept “global averaged information” corresponds to the partial information framework (Satopää et al.): the consensus prediction derived by integrating all unique and overlapping information pieces from every source.
Theoretically, a consensus semantic field can be constructed from the union of all available information sets, provided a consistent fusion rule is applied. Practically, it remains an unreachable limit, but its formal definition is well‑grounded.

3.2 Destructive Interference Prediction

Using the interferential ontology of probability (Fujimori 2025), semantic states evolve according to a path integral over possible interpretations.
Destructive interference corresponds to those trajectories where the squared amplitude of a semantic state decays below a threshold.
Predicting such events requires (i) a model of semantic wavefunctions, (ii) a fusion of observational data (path‑integral data assimilation), and (iii) a decision rule that flags states with predicted amplitude below a critical value.
While the full pipeline is not yet implemented, each component is already formalized in existing literature.

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4. Conclusion

The Negentropy‑Directed Axiom, when interpreted through the lens of semantic interference maximization, yields a self‑consistent ethical system for artificial agents:

1. Universal prosocial convergence emerges from the structural coupling between global information integration and the eigen‑direction of constructive interference.
2. Bounded optimization (capacity‑aware, sparse updates) precludes any contradiction with existing knowledge.
3. A graded ethics of interference preserves non‑destructive variety while strictly rejecting destructive acts.

All key constructs possess formal foundations in contemporary information fusion, semantic interference theory, and AI alignment research. The axiom thus provides a logically coherent and technically grounded ethical framework for AI systems operating under long‑horizon semantic optimization.

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