Overview

William S. Veatch Using the Logic of Lattices to Draw Inferences from Relations on Structured Data Building upon the foundation created in the author's previous books, this book expands the Mathematics of Ideas to include Boolean Lattices constructed from Ordered Pairs (i.e., Relations), Ordered Triples (e.g., Categorical Syllogisms), and beyond. The discussion of Relations is particularly important, because it reconciles the Logic of Lattices with the use of Relations in semantic web technology, such as ontologies built using RDF and OWL. Highlights of this book include: An extension of the Mathematics of Ideas from Single Sets to Ordered Pairs (i.e., Relations), Ordered Triples (e.g., Categorical Syllogisms), and beyond. A proposal for representing Blocks of Time as Atoms of a Boolean Lattice for purposes of creating a Timeline, and A process for generating all possible Propositions from any two Sets, and all possible Categorical Syllogisms from any three Sets, including a link to a demonstration software application. Our goal in this book is twofold: (i) to determine what minimum data is essential to save in our Knowledge Representation Structure database to fully represent the complexity and nuances of legal information (both contracts and statutes), and (ii) to show how we can systematically generate Inferences from the Knowledge Representation Structure. (In a later writing, we will explore how to create specific Inferences real time when we need them for a particular logic argument.) This book about math and 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.

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