Resource Bounded Belief Revision Renata Wassermann Abstract: %Nr: DS-2000-01 %Author: Renata Wasserman %Title: Resource Bounded Belief Revision The problem of belief revision has been extensively studied during the last twenty years. Given an agent with a set of (ascribed) beliefs, how should he change his beliefs when confronted with new information? This is the most general formulation of the problem of belief revision. An agent may be a human being, a computer program or any kind of system to which one can ascribe beliefs and from which one would expect rational reactions. This is a multidisciplinary problem, with applications to several areas. We can give some examples of belief revision as it appears in: * Daily life: I believed it was always raining in Amsterdam. One morning I woke up in Amsterdam and the sun was shining. I believed that on that day the weather was fine, contradicting my previous belief. I had to give up my belief that it always rained there. * Databases: In the database containing data about the customers of a bookstore, there is an entry for John Smith, with his date of birth being 20/2/67. I get then a new order, where John Smith's date of birth is 20/2/76. I cannot add another date of birth and John's date of birth cannot have changed with time. I have to decide what to do. Keep the old data? Substitute it by the new? Or is it another John Smith after all, who should be added to the database? * Robotics: A mobile robot has a map of the environment where it is supposed to move. On the map, there is nothing in front of it, so it should be able to move straight. But then its sensors indicate the presence of a big object in front of the robot. Should it doubt its sensors and continue trying to move straight? Or should it believe its sensors and doubt the map? * Diagnosis: I believe that if I put an article at the right position on a properly working copying machine, I get copies of the article. Suppose I put an article at the right position, but all I get are blank pages. Should I give up my belief that I chose the right position? Or should I give up the belief that the copying machine is working properly? Belief revision has been extensively studied in philosophy for extremely idealized agents. The agents considered are infinite beings, without any limitation of memory, time, or deductive ability. However, adapting these solutions to less idealized agents is far from trivial. In order to solve the problems cited above in a way which can be used by real agents, one has to consider that any realizable agent is a finite being and that calculations take time [Che86]. We need a theory which takes these characteristics -- finiteness, memory and time limitations -- into account. Departing from the standard logical model for belief revision, the main goal of the present work is to find a theory that can be applied to more realistic agents. We stress here that our purpose is not to find a computational implementation of existing theories, but to elaborate a theory for less idealized agents. In a recent paper, Chopra and Parikh [CP99] presented some desiderata for a belief revision formalism which we also see as our goals: distinction between explicit and implicit beliefs, no trivialization in the presence of inconsistencies, computational tractability, and minimal change. The main achievements of our work are: 1. Formalization of a richer notion of belief state, based on the informal works of Harman and Cherniak (Chapter 4). 2. Generalization of standard results found in the literature, allowing for the use of more general logics (Chapter 5). This part is joint work with Sven Ove Hansson. 3. Design of a psychologically motivated, computationally efficient method for focussing on the relevant part of a belief state (Chapter 6). 4. Application of the developed framework to the problem of model-based diagnosis and use of the computational tools from model-based diagnosis for implementing belief revision operators (Chapter 7).