Stablecoins are digital assets designed to maintain a stable value, typically pegged to traditional currencies. Despite their growing prominence, many stablecoins have struggled to consistently meet stability expectations, and their underlying mechanisms often remain opaque and challenging to analyze. This paper focuses on the DAI stablecoin, which combines crypto-collateralization and algorithmic mechanisms. We propose a formal logic-based framework for representing the policies and operations of DAI, implemented in Prolog and released as open-source software. Our framework enables detailed analysis and simulation of DAI's stability mechanisms, providing a foundation for understanding its robustness and identifying potential vulnerabilities.