DIAGRAMMATIC REASONING IN AI Robbie Nakatsu A JOHN WILEY & SONS, INC., PUBLICATION DIAGRAMMATIC REASONING IN AI DIAGRAMMATIC REASONING IN AI Robbie Nakatsu A JOHN WILEY & SONS, INC., PUBLICATION Copyright © 2010 by John Wiley & Sons, Inc. All rights reserved Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750–8400, fax (978) 750–4470, or on the web at www.copyright.com. 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Q335.N355 2009 006.3–dc22 2009015920 Printed in the United States of America 10987654321 CONTENTS PREFACE vii CHAPTER 1 INTRODUCTION: WORKING AROUND THE LIMITATIONS OF AI 1 CHAPTER 2 MENTAL MODELS: DIAGRAMS IN THE MIND’S EYE 23 CHAPTER 3 TYPES OF DIAGRAMS 57 CHAPTER 4 LOGIC REASONING WITH DIAGRAMS 108 CHAPTER 5 RULE-BASED EXPERT SYSTEMS 143 CHAPTER 6 RULE-BASED REASONING WITH DIAGRAMS 188 CHAPTER 7 MODEL-BASED REASONING 228 CHAPTER 8 INEXACT REASONING WITH CERTAINTY FACTORS AND BAYESIAN NETWORKS 264 CHAPTER 9 A FRAMEWORK FOR UNDERSTANDING DIAGRAMMATIC REASONING 302 INDEX 321 v PREFACE This book is really the end product of over a decade of work, on and off, on diagrammatic reasoning in artificial intelligence (AI). In developing this book, I drew inspiration from a variety of sources: two experimental studies, the devel- opment of two prototype systems, an extensive literature review and analysis in AI, human–computer interaction (HCI), and cognitive psychology. This work especially contributes to our understanding of how to design the graphical user interface to support the needs of the end user in decision-making and problem- solving tasks. These are important topics today because there is an urgent need to understand how end users can cope with increasingly complex information technologies and computer-based information systems. Diagrammatic represen- tations can help in this regard. Moreover, I believe that reasoning with diagrams will become an important part of the newest generation of AI systems to be developed in the future. I began investigating the topic of diagrammatic reasoning several years ago as a doctoral student while working on research on user interface design. Almost serendipitously, I stumbled on a concept in cognitive psychology known as mental models. This is the idea that we construct models of the world in our minds to help us in our daily interactions with the world. I was intrigued by the idea and wanted to learn more about how, when, and why people do this. I believed that if we could better understand what these mental models are about, then we might use this knowledge to design computer user interfaces and aids, such as tutorials and explanations that might support people in complex tasks, and in their everyday lives. I devote an entire chapter (Chapter 2) to the subject of mental models. It turns out that my investigation on mental models naturally and gradually evolved into a more general investigation on diagrams. This is because I soon vii viii PREFACE came to view mental models, in many cases, as nothing more than diagrams in the mind’s eye. By diagram I mean a graphical representation of how objects in a domain are interconnected or interrelated to one another. (In Chapter 3 I try to pin down the concept of diagram by defining it more precisely. I also provide a taxonomy of diagram types.) In the process of researching and studying diagramming, I made a few key discoveries. The first is that diagramming is really a basic human activity—most of us do it quite naturally, even if in an informal and adhoc way. On occasion, we do it more formally and explicitly and will spend time to create the “right” diagram, especially if we need to present it to others. I was surprised at how often the need to diagram appeared in my own daily life; it was not at all difficult to come up with several examples of diagramming. The second discovery is that diagramming can take on numerous incarnations and forms, more than I could ever imagine. It was overwhelming to keep track of all the different notations and techniques. Yet, underlying all these variations in notation were a few underlying principles and themes. I will address what these principles and themes are later on in Chapter 3 and in the concluding chapter, Chapter 9. The third discovery is that a diagram is more than just a static picture or representation. Diagrams can be used in more dynamic and interesting ways. Indeed, a theme of this book is that diagrams can be a central part of an intelligent user interface, meant to be manipulated and modified and, in some cases, used to infer solutions to difficult problems. All in all, there is much more to diagramming than meets the eye. What were my motivations for writing this book and what message do I want to convey to the reader? First, I wanted to understand how diagrams can be used to help learners understand complex ideas. As a teacher at an institution of higher education, I am particularly interested in the pedagogical function of diagrams—to teach and communicate complex ideas with precision and clarity. I am keenly aware of the difficulties that students face in the classroom in trying to understand course material. Textbooks, all too often, contain explanations that confuse more than edify, and classroom lectures often fail to communicate effectively because instructors make too many assumptions about what students are supposed to know or what they already know. In the end, the classroom environment fails to create an effective mental model of the course material for the learner. Moreover, interconnections and interrelationships among concepts are not reinforced strongly enough, so that retention of the material is short lived. Throughout this book, I present many examples of how diagramming can be used to convey information more effectively to learners. A second motivation is to understand how to make AI systems easier to understand and use. This is really one of the primary objectives of the book. Many critics of AI systems have argued for more transparency and flexibility in the user interface if users are to embrace and accept these systems. Traditional intelligent systems are black box systems that provide little or no opportunity to actively probe and question system conclusions and recommendations. Therefore, I argue that a diagrammatic user interface can help users better understand and visualize system actions. PREFACE ix To this end, I borrow heavily from AI and hence the title of the book is Diagrammatic Reasoning in AI . I could just as easily have titled the book simply “Diagrammatic Reasoning” or “The Visualization of Expertise,” but these titles do not adequately capture how much I have borrowed from the AI discipline. I look, specifically, at expert systems, model-based reasoning, and inexact reasoning (including certainty factors and Bayesian networks)—three important AI areas that have attempted to create programs capable of emulating human thinking and problem solving in various ways. I also cover logic reasoning (Chapter 4), which is a topic that has also been dealt with extensively in the AI literature. A third motivation for writing this book is that there are no books that I know of on the marketplace today that address diagrammatic reasoning in a coherent or unified way. I hope to fill this void by providing a more cohesive treatment of the subject. While there are a number of books about information design and graphic design that deal with the topic of diagramming, they explore the topic primarily from the perspective of illustrating principles of good graphic design. There are also several books that deal with specific diagramming notations.