  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.
