INTEGRATING DISCRETE AND CONTINUOUS CHANGE IN A LOGICAL FRAMEWORK

The goal of our work is to develop theoretical foundations for the rep resentation of knowledge in domains in which properties may vary conti nuously. One achievement of our research is that it extends the applic ability of current research on theories of action. Furthermore, we are able to apply known approaches to the frame and ramification problems , developed for discretely changing worlds, to domains in which the wo rld changes continuously. Our approach is based on the discrete situat ion calculus and on a monotonic solution to the frame problem. In orde r to address the combined frame and ramification problems, we extend L in and Reiter's work. We use Pinto and Reiter's extension to the situa tion calculus to represent occurrences. We extend this work further to allow for reasoning by default. For example, if we know that a ball i s falling and we do not have any reason to believe that an action woul d interfere with the ball's motion, then we assume that the ball will hit the ground. Finally, we extend the language of the situation calcu lus to allow for properties that change within situations. We also sho w that our proposed situation calculus inherits the solutions to the f rame and ramification problems.