Le Nozze di Giustizia. Interactions between Artificial Intelligence, Law, Logic, Language and Computation with some case studies in Traffic Regulations and Health Care

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.