Can artificially intelligent systems follow rules? The answer might seem an obvious 'yes', in the sense that all (current) AI strictly acts in accordance with programming code constructed from highly formalized and well-defined rulesets. But here I refer to the kinds of rules expressed in human language that are the basis of laws, regulations, codes of conduct, ethical guidelines, and so on. The ability to follow such rules, and to reason about them, is not nearly as clear-cut as it seems on first analysis. Real-world rules are unavoidably rife with open-textured terms, which imbue rules with a possibly infinite set of possible interpretations. Narrowing down this set requires a complex reasoning process that is not yet within the scope of contemporary AI.This poses a serious problem for autonomous AI: If one cannot reason about open-textured terms, then one cannot reason about (or in accordance with) real-world rules. And if one cannot reason about real-world rules, then one cannot: follow human laws, comply with regulations, act in accordance with written agreements, or even obey mission-specific commands that are anything more than trivial. But before tackling these problems, we must first answer a more fundamental question: Given an open-textured rule, what is its correct interpretation? Or more precisely: How should our artificially intelligent systems determine which interpretation to consider correct? In this essay, I defend the following answer: Rule-following AI should act in accordance with the interpretation best supported by minimally defeasible interpretive arguments (MDIA). In Section 2, I will introduce and defend the need for AI which can produce interpretations of rules that are supported by interpretive argumentation, and advocate for AI that is argument-justified rather than merely explainable. But in order to recognize interpretive argument quality, we need a way to estimate argument strength. Section 3 argues that the minimal defeasibility standard is our best hope. Finally, I address anticipated counterarguments and possible points of confusion in Section 4.