An important aim of this paper is to convey some basics of mathematical logic to the legal community working with Artificial Intelligence. After analysing what AI is, we decide to delimit ourselves to rule-based AI leaving Neural Networks and Machine Learning aside. Rule based AI allows for Formal methods which are described in a rudimentary form. We will then see how mathematical logic interacts with legal rule-based AI practice. We shall see how mathematical logic imposes limitations and complications to AI applications. We classify the limitations and interactions between mathematical logic and legal AI in three categories: logical, computational and mathematical. The examples to showcase the interactions will largely come from European traffic regulations. The paper closes off with some reflections on how and where AI could be used and on basic mechanisms that shape society.

翻译：本文的重要目标在于向从事人工智能研究的法律界人士传达数理逻辑的基本概念。在分析何为人工智能后，我们决定将研究范围限定于基于规则的人工智能，暂不涉及神经网络与机器学习。基于规则的人工智能能够采用形式化方法，本文将以初步形式对其进行阐述。随后我们将探讨数理逻辑如何与基于规则的法律人工智能实践相互作用，并揭示数理逻辑对人工智能应用施加的限制与复杂性。我们将数理逻辑与法律人工智能之间的限制及相互作用划分为三类：逻辑性限制、计算性限制与数学性限制。相关案例主要来自欧洲交通法规。文章最后就人工智能可能的适用领域及方式，以及塑造社会的基本机制进行了若干反思。