REFINING THE SEMANTICS FOR EPISTEMIC LOGIC PROGRAMS by Patrick Thor Kahl, M.S. A Dissertation in COMPUTER SCIENCE Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY Approved Richard Watson Chair of Committee Michael Gelfond Yuanlin Zhang Mark Sheridan Dean of the Graduate School May 2014 Copyright © 2014 by Patrick Thor Kahl To my family \Exploit symmetry whenever possible. Do not destroy it lightly." |Edsger Dijkstra (1930-2002) Texas Tech University, Patrick Thor Kahl, May 2014 ACKNOWLEDGMENTS My sincere thanks to the members of my committee who were all instrumental in the success of my research goal. My advisor, Dr. Richard Watson, who kindly agreed to take me in as his doctoral student, was a pleasure to work with on this topic. I appreciate all the hours he spent guiding me, sharing the ups and downs of one after another failure, yet maintaining the fervent belief that we were ever closer to our goal. In short, he was able to make this task an exciting endeavor, sharing with me in the adventure of scientific research. It was Dr. Michael Gelfond who introduced Epistemic Specifications to the world in the early 1990s, and he has continued to lead in its development, particularly in recent years with the increase in interest. His keen insight concerning the various different modal reducts proposed and whether they reflected how a rational agent should pick from among different models kept me from abandoning what eventually became the definition presented herein. The new definition led to a new intuition concerning the world views of various programs, one that I now believe is correct and also beautiful. Dr. Gelfond has continued to be my mentor since my undergraduate years at the University of Texas at El Paso. Anyone who has worked with him has indeed been blessed. Dr. Yuanlin Zhang continued to support me in my ever-changing directions, pa- tiently listening to my ideas and helping guide me toward realistic goals. He was the only one who was able to come up with a methodology that successfully addressed the problem of circular support through modal operator M as originally perceived. Although what I eventually chose to propose in this dissertation does not use his methodology, he addressed the objective I had at the time, and his idea remains a promising approach for future research. He has been both a teacher and a friend, giving me that most precious commodity, his time. I also wish to express my appreciation to the past and present members of the Knowledge Representation Lab at Texas Tech for their support, suggestions, encour- ii Texas Tech University, Patrick Thor Kahl, May 2014 agement, and friendship. Everything from KR seminars to ping-pong was made more enjoyable and edifying due to their participation. I humbly follow in the footsteps of greats|Marcello, Veena, Sandeep, Ricardo, Yana, Weijun, Daniela, Justin|whose accomplishments have been an inspiration. I am especially grateful to my most recent lab mates|Evgenii, Edward, and Qianji|for their assistance and unending patience with me. My best wishes to them in their research endeavors. (And, yes, I'll miss the basement dwellers. You know who you are.) My thanks also goes out to Dr. Nelson Rushton who further enlightened me con- cerning the language of mathematics and mathematical rigor in the field of computer science. His teachings have helped me improve the clarity of my communications, though I realize that I still have much to learn. Further thanks is extended to the faculty, staff, and fellow students of the Depart- ment of Computer Science who taught, assisted, laughed, struggled, worked with, and shared in my many experiences here at Texas Tech. Finally, to my dear family, I thank you with all my heart. The support I received from my mother, my siblings, and my extended family|Lara, Michael, and Greg| enabled me to feel good about pursuing this goal so late in my life. My wife Yulia and my children Alexandra and Jonathan all persevered through the years of my return to school. Their never-ending love, encouragement, support, and patience during this time have made it all possible. Patrick Thor Kahl March 12, 2014 Department of Computer Science Texas Tech University Lubbock, TX, USA iii Texas Tech University, Patrick Thor Kahl, May 2014 TABLE OF CONTENTS ACKNOWLEDGMENTS . ii ABSTRACT . vi I INTRODUCTION . .1 1.1 Motivation for a New Definition . .3 1.2 Finding the New Definition . .5 II BACKGROUND . .7 2.1 ASP . .7 2.2 Epistemic Specifications . .9 2.3 Language Development Timeline . 10 III SYNTAX AND SEMANTICS OF EPISTEMIC SPECIFICATIONS 13 3.1 Syntax . 13 3.2 Semantics . 15 IV AN ALGORITHM FOR FINDING WORLD VIEWS . 21 V SIMPLIFYING AN EPISTEMIC LOGIC PROGRAM . 24 VI COMPARISON WITH OLD VERSIONS OF THE LANGUAGE . 25 6.1 Semantic Differences between Old and New Language . 25 6.2 Expressibility . 26 VII APPLICATIONS . 28 VIII RELATED WORK . 32 IX CONCLUSIONS AND FUTURE WORK . 35 9.1 Conclusion . 35 9.2 Future Work . 35 BIBLIOGRAPHY . 41 APPENDIX A: PROOFS . A-1 APPENDIX B: FAILED ATTEMPTS TO FIND CORRECT SEMANTICS B-1 B.1 Failed Attempt 1 . B-2 B.2 Failed Attempt 2 . B-2 iv Texas Tech University, Patrick Thor Kahl, May 2014 B.3 Failed Attempt 3 . B-3 B.4 Failed Attempt 4 . B-4 B.5 Failed Attempt 5 . B-5 B.6 Failed Attempt 6 . B-6 B.7 Failed Attempt 7 . B-6 APPENDIX C: EPISTEMIC LOGIC PROGRAMS WITH SORTS . C-1 C.1 Introduction . C-1 C.2 Syntax and Semantics . C-2 C.2.1 A New Meaning for Rules with Variables . C-2 C.2.2 Syntax of an ELPS . C-3 C.2.3 Semantics . C-4 C.3 Algorithm . C-4 APPENDIX D: EXAMPLE PROGRAMS . D-1 v Texas Tech University, Patrick Thor Kahl, May 2014 ABSTRACT The primary goal of this dissertation is to present a new semantics for the lan- guage of Epistemic Specifications that accurately defines those models of associated programs that are to be considered as world views from the standpoint of a rational agent. Epistemic Specifications is a declarative programming language that is an ex- tension of answer set programming (ASP) through the addition of modal operators K and M. Programs written in this language are called epistemic logic programs. Previously proposed semantics did not satisfy our intuition for certain programs. In order to achieve the stated goal, the semantics should reflect the principles of a rational agent, as well as our intuition regarding the notion of support for a literal. Toward that goal, the focus here is on the following items. First, a new definition is proposed for the modal reduct of a program with respect to a collection of sets of literals. This is used to define models of a program that are accepted as its world views. Among other things, the new definition adds insight into a preference held by a rational agent when deciding between models that are based on different forms of extended literals. Second, an algorithm is proposed for finding the world views of an epistemic logic program under the proposed semantics. The algorithm was designed to take advantage of current state-of-the-art ASP solvers. A proof-of- concept implementation demonstrates its effectiveness. Finally, a framework for a conformant planner written in the language of Epistemic Specifications is introduced. Combined, these show real promise for the practical use of epistemic logic programs. Included in this dissertation is a history of Epistemic Specifications and an account of many failed attempts to “fix” the semantics. Also included is a list of example programs and their associated world views. These programs represent some of the more challenging problems and are believed useful in verifying the correctness of any proposed semantics as well as algorithms and their implementations. Many of these example programs come as a result of experience gained from failed attempts to find a solution to the so-called \unintended world views" problem. vi Texas Tech University, Patrick Thor Kahl, May 2014 CHAPTER I INTRODUCTION We define a new semantics for the language of Epistemic Specifications, an ex- tension of the language of answer set programming (ASP) that was introduced in the early 1990s by Michael Gelfond [Gelfond, 1991, Gelfond, 1994]. The language of Epistemic Specifications allows for introspective reasoning through the use of modal operators K and M. A literal preceded by a modal operator is called a subjective literal. Subjective literal K p can be understood to mean "p is known." M p can be understood to mean \p may be believed." We believe the semantics proposed herein better addresses the principles that a rational agent should uphold when deciding which models of a program should be accepted and which should be rejected. Among the principles that we wish to address is the belief that a rational agent should only believe what he is forced to believe based on the rules of the program. What is meant by \based on the rules of the program" is that one or more rules combined should provide the justification—a clear argument of support|for literals being present in a belief set among the collection of belief sets in a world view of the program. The primary difficulty has been to formalize this notion of support as it applies to a literal in a program, particularly when it is caught up in a dependency cycle due to recursive rules involving subjective literals. It is hoped that the definitions presented here will provide a satisfactory semantics for the language, a quarry that has evaded us for two decades.