This book, the expanded and completely revised text of the author's renowned 1993 dissertation, studies the logical aspects of legal reasoning, in order to provide philosophical foundations for legal applications of Artificial Intelligence. It respects that legal reasoning often takes place in a disputational setting, and observes that the law leaves ample room for disagreement, which means that lawyers reason under the possibility of exceptions and with contradictory legal sources, and cannot do without non-deductive reasoning forms, such as analogical reasoning. The study shows that, contrary to what is often said, these features do not escape a logical analysis if recent developments in logic and Artificial Intelligence on so-called non-monotonic reasoning and defeasible argumentation are used, and if logic is regarded as a tool in, rather than as, a model of legal argument. This book is relevant for scholars in legal philosophy, artificial intelligence, logic and argumentation theory, and can also serve as a textbook for graduate courses in AI & Law, non-monotonic reasoning and legal argumentation.