William S. Veatch The New Logic of the Law Vol. 1 - Building a Foundation for Artificial Intelligence Applications in the Law This book explores a "New Logic of the Law" based upon set theory. The concept is that every "Idea" is either an Atom (i.e., an Idea that cannot be broken down further) or a Compound. Once we accept that an Idea is either an Atom or a Compound, then we can create Sets of Ideas. In fact, the Power Set of an Idea, i.e., the set of all subsets including the set itself and the empty set, together with the operations of Union, Intersection, and Complementation, forms a Boolean Algebra and an equivalent Boolean Lattice. The New Logic of the Law is based upon the logic inherent in the Boolean Lattice structure. Building upon the foundation created in the author's previous books, "Math Without Numbers" and "Propositional Logic as a Boolean Algebra - A New Perspective," this book establishes a system of logic that is robust enough to serve as the foundation for artificial intelligence software applications for use by practicing lawyers. The book reviews existing systems of logic, including the categorical syllogism of Classical Logic, propositional logic, compound arguments, and predicate logic. The book then goes on to demonstrate that the logic of Boolean Lattices subsumes these existing forms of logic, and then goes much further. At the end of each Chapter is a section entitled "what the practicing lawyer needs to know." In this way, the lawyer who does not want to understand the underlying mathematics and logic can still benefit from reading the book and learn to use the tools of the New Logic of the Law. This book about Logic is written by a practicing attorney, for use by practicing attorneys. It should also be of interest to anyone involved in creating artificial intelligence software applications for use in the practice of law.