On the projection problem in active knowledge bases with incomplete information

Abstract

The problem of projection has been identified as a fundamental reasoning concern in dynamical domains, where we are to determine whether or not some conditions will hold after a sequence of actions has been performed starting in some initial state. Solving the problem requires, at the very least, effectively reasoning about how actions transform the world, and inferring the logical consequences of the initial knowledge base Completing this Ph.D. has been an enriching journey. What follows is my humble attempt to thank those who have been a part of this ride, through its many potholes. Let me begin by expressing my sincere gratitude to Professor Gerhard Lakemeyer, for first encouraging me to find my own path, and then offering valuable suggestions to realize my goals. My previous background was in machine learning, and I imagine my initial intuitions about epistemic logic must have seemed peculiar. In spite of that, Gerhard patiently helped me fix my technical knowledge, allowed me to explore tangential ideas freely, and more importantly, shared his thoughts on what makes a problem interesting. He has overseen my academic growth for the past four years, and his views on mathematical logic and artificial intelligence have greatly influenced my own. For all of this, for showing me how to write scientifically, and for your continued guidance and support: thank you. A special thanks also goes to my external examiner Professor Hector Levesque for painstakingly reading this thesis, and bringing significant bugs and typographical errors to my attention. Carrying out my work at the Knowledge-based Systems Group has been a lot of fun. I thank its members for great corridor and coffee conversations. Participating in soccer matches, and doctoral seminar escapes to picturesque countrysides, with the remainder of Informatik 5 was very exciting, and I hope these traditions are here to stay. I also thank Jens Claßen for technical discussions, and Tim Niemüller for offering to translate the abstract of this thesis. A number of people visited the department over the years, and among them, I would especially like to thank Yongmei Liu for insightful conversations on research. She also had shared her intuitions about "forgetting" with me, which prompted me to explore that topic. I thank her for this. Financial support for the years 2008-2010 was gratefully received by the Deutsche Forschungsgemeinschaft (German Research Foundation), which funded the graduate school Software for mobile communication systems, of which I was a stipendiary. During my time at the graduate school, Prof. Otto Spaniol provided constant encouragement, and supported our participation in Dagstuhl seminars. For this, I am thankful. Further, Prof. Wolfgang Thomas encouraged me to present my results to the AlgoSyn graduate school, and for this, I thank Wolfgang. For much of the year 2011, financial support was received by the BIT research school, and for this I express my gratitude to Gerhard and Prof. Matthias Jarke. For the remainder of 2011, financial support w...