Lecture Notes in Artificial Intelligence

Transcription

1 Lecture Notes in Artificial Intelligence 1409 Subseries of Lecture Notes in Computer Science Edited by J. G. Carbonell and J. Siekmann Lecture Notes in Computer Science Edited by G. Goos, J. Hartmanis and J. van Leeuwen

2 Torsten Schaub The Automation of Reasoning with Incomplete Information From Semantic Foundations to Efficient Computation Springer

3 Series Editors Jaime G. Carbonell, Carnegie Mellon University Pittsburgh, PA, USA J0rg Siekmann, University of Saarland, Saarbriicken, Germany Author Torsten Schaub Universit~it Potsdam, Institut fiir lnformatik Postfach , D Potsdam, Germany Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Sehaub, Torsten: The automation of reasoning with incomplete information : from semantic foundations to efficient computation / Torsten Schaub. - Berlin ; Heidelberg ; New York ; Barcelona ; Budapest ; Hong Kong ; London ; Milan ; Paris ; Santa Clara ; Singapore ; Tokyo : Springer, 1998 (Lecture notes in computer science ; Vol : Lecture notes in artificial intelligence) ISBN CR Subject Classification (1991): 1.2.3, 1.2, F.4.1 ISBN Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. 9 Springer-Verlag Berlin Heidelberg 1997 Printed in Germany Typesetting: Camera ready by author SPIN / Printed on acid-free paper

4 Preface "Almost no plan is guaranteed, no utterance utterly unambiguous, no rule without exception -- there's no such thing as a sure thing." David W. Etherington, 1986 Reasoning with incomplete information constitutes a major challenge for any intelligent system. In fact, we expect from such systems that they are not paralyzed by missing information but rather arrive at plausible results by bridging the gaps in the available information. There are moreover situations in which it is necessary to act despite incomplete information. In a word, intelligent systems have to provide means for reasoning in the absence of total information. The automation of this form of reasoning is the subject of this book. A versatile way of reasoning in the absence of information is to reason by default. In this manner, we overcome a lack of information by making default assumptions about a situation at hand. Default reasoning puts faith in standard situations that are free from strangeness and unexpectedness; it relies on general rules expressing anticipated states of affairs. A formalization of this form of reasoning is furnished by default logic -- a logical system developed by Raymond Reiter in [Rei80]. This book aims at providing formal and practical means for automating reasoning with incomplete information by starting from the approach taken by default logic. For this endeavor, we span a bridge between formal semantics, over logical systems for default reasoning, to efficient implementations.

5 Acknowledgments The act of expressing gratitude constitutes a privilege and a pleasure for everybody finishing a long piece of work. It is then a great source of satisfaction to lean back and think about all the little victories and defeats one was able to share with other people. However, such an account becomes longer and longer over the years and it bears the danger of overlooking many people that merit an acknowledgment but are not explicitly honored. Thanks to all of you! Nonetheless, I would like to express particular gratitude to those that are on the top of my mind: First of all, I would like to thank my family and my friends. They never appear on the acknowledgments of a research paper but nonetheless bear many resulting moods. Thank you, Susanne and Larissa. You make all this worthwhile! A big hug is also due to my parents and grandparents who were always there when I needed them and who provided me with more than I deserved. I miss them all the more these days. I am indebted to Philippe Besnard, Wolfgang Bibel, James Delgrande, and Josef Schneeberger, who supported me with advice, friendship, and encouragement. They have all enriched my scientific and personal career in a very lasting way: I would like to thank Philippe for the patience he had when clarifying my early (and even later) ideas, for his hospitality, and the fun we had, have, and will have! Philippe is not only an excellent researcher, he is also excellent in teaching how to research. I am indebted to Wolfgang Bibel for his encouragement, his constant support, and the time he spent on improving the presentation of many manuscripts. I would like to thank Jim for his support and hospitality, for all the intuitions he shared with me, his patience in office-sharing and correcting my English, and finally all the hugs he allowed me to hand over the ocean. I would like to thank Josef for his friendship and his lasting support from the very early days. Without them, I would be someone else somewhere else. I gratefully acknowledge the significant contributions of all people with whom I had the pleasure of working together, in particular the co-authors of my research papers, namely Antje Beringer, Philippe Besnard, Wolfgang Bibel, Gerd Brewka, Stefan Briining, James Delgrande, Christine Froidevaux, Steffen H611dobler, Thomas Linke, Ken Jackson, Gerd Neugebauer, Pascal Nicolas, Aaron Rothschild, and Michael Thielscher. Thanks for your time, your ideas, and your inspiration! In fact, this monograph describes the outcome of a research program that I have been able to pursue since As a matter of fact, a salient part of this book stems from material taken from my dissertation thesis [Sch92a] carried out at the Technical University of Darmstadt, Germany, and my habilitation thesis [Sch95a] accomplished at IRISA, Rennes, France. Therefore, I would like to take this opportunity to express my great appreciation to the members of the my dissertation committee: Peter Kammerer, Wolfgang Bibel, Alejandro Buchmann, James Delgrande, Jos6 Encarna~o, and Rtidiger Reischuk, and to those of my habilitation committee: Jean-Pierre Ban~tre, Wolfgang Bibel, Patrice Enjalbert, Christine Froidevaux, Philippe Besnard, Jean-Paul Delahaye, and Jean-Claude Raoult. I thank all of you

6 VIII Acknowledgments for sharing with me and supporting me on the occasion of these decisive events of my scientific career! I would like to thank all my friends within the Intellectics group at Darmstadt for many fruitful and not so fruitful discussions, for many Hiitli sessions and lots of fun. Among them, a big hug goes to Maria, who always lent a helping hand. Thanks for the great time, Gene, Matthias, Sepp, Stebr, and, of course, Uwe! Thank you Steffen for kicking me at the right time. My Darmstadt days are inseparably connected with the TASSO project, providing a great research environment that was particularly stimulating due to many fruitful discussions, in particular those on nonmonotonic reasoning with Gerd Brewka and Ulrich Junker. In fact, it was Gerd who introduced me to many problems I have been working on in the last few years. In the same way, I would like to express my warmest thanks to my friends in the REPCO group at IRISA, Rennes, who moreover had to endure my (early) French along with many "petits caf6s dans des grandes tasses". M'enfin! Merci pour votre aide, Evelyne, MaO, Pascale, Ren6, fylvie et ~Uric! Last, but not least at all, I'm indebted to my friends and colleagues at the University of Angers, in particular, the members of my group for their constant support and encouragement! Merci Beatrice, Gilles et Pascal de m'avoir toujours d6broulli6. Saint Barth616my d'anjou, Spring 1996 Torsten Schaub This research was partially supported by the German Federal Ministry for Research and Technology within project TASSO under grant number ITW 8900 C2 and by the Commission of the European Communities within the program "Human Capital and Mobility" under grant number ERB4001GT The author moved to the University of Potsdam during the printing phase of this monograph.

7 Table of Contents Preface... Acknowledgments... V VII. Introduction The plan of the book The book in context Preliminaries The original approach: Classical default logic Formal properties Restricted default theories A semantics for classical default logic An alternative approach: Constrained default logic Motivation Constrained default logic ,3 Formal properties The focused models semantics Variations of constrained default logic Conclusion Putting default logics into perspective Variants modifying the notion of consistency A guiding example Justified default logic Constrained default logic: Revisited ,1.4 Rational default logic Variants recording consistency assumptions Cumulative default logic Variants of cumulative default logic ,3 Other Variants ,4 Conclusion... 51

8 X Table of Contents. A context-based framework for default logics Motivation Contextual default logic Embedding existing default logics Formal properties Conclusion Possible worlds semantics for default logics Motivation Possible worlds semantics for constrained default logic Possible worlds semantics for classical default logic Possible worlds semantics for justified default logic Possible worlds semantics for contextual default logic Conclusion Adding specificity to default logics Motivation Determination of specificity information Compiling specificity into default theories Conclusion Adding lemma handling to default logics Motivation Lemma handling in constrained default logic Lemma handling in classical default logic Conclusion Query-answering in default logics Motivation Computational characterizations A method for query-answering in default logics The connection method Complementarity Admissibility Compatibility Characterizing default proofs Implementing the approach An algorithm A preliminary case-study An incremental approach An alternative characterization of extensions Incremental compatibility An incremental algorithm Discussion Experiments

9 Table of Contents XI A straightforward implementation Implementations separating compatibility Implementations integrating compatibility Extensions Integration of lemma handling Model-based consistency-checking Skeptical query-answering Conclusion A Prolog-technology compiler for query-answering Motivation Implementing query-answering Extensions and implementation Conclusion Conclusions and perspectives A. Appendix A. 1 Original definition of rational extensions A.2 Modal logic References