AEon Formalism: Logic of Existence (LoE): Relational Operators, Logos, and Emergent Governance

Title:

AEon Formalism: Logic of Existence (LoE) — Relational Operators, Logos, and Emergent Governance

Description:

This work presents a formal development of the Logic of Existence (LoE) — a relational, non-ontological framework for analyzing emergence, conflict, coherence, and governance in complex systems.

LoE treats existence not as a property of isolated entities, but as a function of relational persistence under tension. The framework is developed at the operator level and avoids psychological, metaphysical, and narrative assumptions. All constructs are defined structurally and processually.

The document introduces:

a minimal relational operator calculus based on boundaries, intersections, metastability, and Logical Time;

a formal distinction between logos (conflict-preserving, generative dynamics) and anti-logos (eliminative, collapse-driven dynamics);

canonical operator graphs (unweighted and weighted) suitable for computational interpretation;

logos-consistent design rules for AI architectures, including separation of space generation (e.g. GPU substrates) from logic emergence;

process-level Logos Archetypes (Mill, Filter, River, Vortex) modeling meaning as survival under dynamics rather than symbolic evaluation;

the Helical Logos Archetype as a model of intelligence emerging from sustained relational difference without collapse;

formal theorems describing transitions from logos to anti-logos (violence) and conditions for logos-compatible governance;

a non-destructive reform path from anti-logos to logos-compatible governance structures;

a simulation sketch showing how governance reform can be modeled on the LoE operator graph using Logical Time and metastability criteria.

The work is intended for researchers in theoretical AI, complex systems, governance modeling, and relational formalisms. It does not propose a normative ideology or a closed ontology. Instead, it offers a compact formal language for reasoning about when systems remain generative and when they collapse due to forced resolution of conflict.

Author:

Krzysztof Sawa

Tilburg, The Netherlands

Date:

26 January 2026

License:

Creative Commons Attribution–NonCommercial–NoDerivatives 4.0 International (CC BY-NC-ND 4.0)

Keywords:

Logic of Existence, LoE, Logos, Anti-Logos, Relational Operators, Logical Time, Emergence, AI Architecture, Complex Systems, Governance