Towards a fundamental theory of modeling discrete systems

2025-08-27

AI Summary

Discrete system modeling in the digital era faces a foundational theoretical gap. This paper proposes Heraklit, a novel modeling framework that integrates philosophical inquiry with formal methods to establish a new abstraction paradigm for discrete systems. Departing from traditional continuity assumptions, Heraklit adopts dynamic flux as its ontological foundation and rigorously defines core concepts—including modeling correctness, the nature of information, and structural invariance. Its key contributions are threefold: (1) it formally axiomatizes Heraclitus’s “panta rhei” (“everything flows”) principle into a computationally tractable modeling foundation; (2) it establishes modeling as a fundamental discipline in the digital age; and (3) it provides an extensible theoretical architecture that unifies and enables future advances in modeling verification, semantic information modeling, and invariance analysis.

Technology Category

• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Knowledge Representation and Reasoning: Other Foundations of Knowledge Representation & Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Modeling is a central concern in both science and engineering. However, we need a new fundamental theory to address the challenges of the digital age. In this paper, we first explain why modeling is fundamental and which challenges must be addressed in the digital world. As a main contribution, we introduce the Heraklit modeling framework as a new approach to modeling. We conclude with some general remarks. Future work will involve the correctness of modeling, the notion of information, and the description of invariance in modeling.

Problem

• Developing a fundamental theory for modeling discrete systems
• Addressing digital age challenges in scientific and engineering modeling
• Introducing a new modeling framework for discrete systems

Innovation

• Introduces Heraklit modeling framework
• Addresses digital age modeling challenges
• Focuses on correctness and information theory