Contradiction‑Driven Behaviour in Rule‑Based Systems: A Structural Model with a Natural Worked Example

This publication introduces a structural model for analysing behaviour in rule‑based systems under contradictory constraints. The model treats rules as deterministic requirements and shows how incompatible requirements can generate looping behaviour, stalls, collapses, and reset conditions. The framework is domain‑independent and focuses on the interaction between requirements, contradictions, and transitions rather than psychological or biological assumptions. To demonstrate the model in practice, the document includes a worked example based on the ant death loop, a natural phenomenon in which ants become trapped in a self‑reinforcing circular pheromone trail. The example illustrates how a simple rule set can produce an unresolvable contradiction that forces the system into a stable loop state. The analysis shows why the loop persists, how it self‑reinforces, and what external conditions are required to break it. The publication is intended as a clear and accessible introduction to contradiction‑driven behaviour, providing both a general framework and a concrete example that readers can use to understand how deterministic systems behave under incompatible constraints.Primary Category: Mathematical Physics Secondary: Logic, Philosophy of Physics, Systems TheoryResearch Programme Context:This paper is part of an ongoing research programme in mathematical physics, formal logic, and the philosophy of physical systems. The programme includes multiple papers, theoretical tools, and conceptual frameworks that collectively develop a unified operator-based model of emergence, contradiction, and system dynamics.