The Conceptual Model Completeness Conjecture (CMCC) as a Universal Computational Framework

Abstract

The Conceptual Model Completeness Conjecture (CMCC) formally constrains WHAT can be said, before deciding HOW to say it in one or more languages.  The conjecture posits that the declaratively-expressible, finitely-computable, design‑time semantics for Any Conceptual Model can be fully expressed using just 5 simple primitives in a nullable, ACID‑compliant datastore—Schema (S), Data (D), Lookups (L), Aggregations (A), and Lambda Calculated Fields (F)— without external specialized side-car logic, syntaxes, grammars or languages.

Initially conceived for Conceptual Model modeling, CMCC is demonstrated here to be computationally universal, aligning with Lambda Calculus, Rule 110, and Stephen Wolfram’s Principle of Computational Equivalence. We further illustrate CMCC’s capacity to express multiway computational structures, providing a structural analog to Wolfram’s multiway systems and the Ruliad. By extending CMCC to domains such as genetics and physics, we propose that CMCC may represent a fundamental computational substrate underlying various real-world processes. This paper formalizes CMCC’s universality through rigorous mathematical definitions and comprehensive mappings to established computational models, provides diverse case studies, and outlines a path for future research—potentially positioning CMCC as a unified computational foundation for AI, biology, and fundamental physics.

Keywords

CMCC, Computational Universality, Turing Completeness, Multiway Systems, Wolfram’s Principle, Lambda Calculus, Rule 110, Genetics, Physics, ACID, Declarative Semantics, Ruliad, Computational Irreducibility

1. Introduction

1.1 Background

In the quest to develop robust computational frameworks, establishing universality—the capability to model any computable function—is paramount. Turing Completeness serves as a cornerstone in this endeavor, with models like Lambda Calculus, Turing Machines, and cellular automata (e.g., Rule 110) exemplifying this property. Concurrently, the evolution of Conceptual Model modeling has focused on encapsulating the declarative “what” of systems, deferring the imperative “how” to underlying execution engines. This separation of concerns facilitates the creation of flexible, maintainable systems by distinguishing between the specification of desired outcomes and the mechanisms to achieve them.

However, existing Conceptual Model frameworks often rely on domain-specific languages (DSLs) or custom scripts to handle complex logic and behavior, leading to fragmentation and maintenance challenges. This reliance on specialized syntaxes can impede the scalability and adaptability of rule-based systems, particularly as they expand to encompass more intricate domains.