Modeling Dynamical Sytems in the Situation Calculus: Some Representational and Computational Issues for Automated Reasoning Raymond Reiter Department of Computer Science University of Toronto For the past several years, the Cognitive Robotics Group at the University of Toronto has been exploring the feasibility of the situation calculus as a theoretical and computational foundation for modeling dynamical systems. It is a challenging research problem to capture, in a single formal and computational framework, the full range of characteristics associated with such settings: the frame, ramification and qualification problems, exogenous and natural events, chance events and the unpredictability of action effects, complex actions and procedures and the ability of an agent to perform such actions, time, concurrency, hypothetical and counterfactual reasoning about action occurrences and time, perceptual actions and their effects on an agent's mental state, the complex relationships among reasoning, perception and action, planning, belief revision in the presence of conflicting observations, etc. The principal objective of this project is to provide just such a general theory and implementation of actions and time, and, as already noted, our formal foundation for this has been the situation calculus. While we remain far from achieving these long-range objectives, we have had some modest success in this undertaking. Starting with a solution to the frame problem for deterministic, simple actions, we have defined and implemented GOLOG, a novel situation calculus-based logic programming language for defining complex system behaviors, and experimented with it in robotics applications, and for software agents. Recently, GOLOG has been generalized to CONGOLOG and RGOLOG, concurrent languages for representing reactive systems, and multiple processes. There is a situation calculus account of sensing (knowledge-producing) actions, and this has been extended to include noisy sensors. The solution to the frame problem for deterministic primitive actions has been extended to nondeterministic ones. A situation calculus calculus account has been given of planning for agents which can sense their environments. Agent goals and rational actions have been formalized in the situation calculus. Concurrency, natural actions and continuous time have all been given situation calculus-based accounts, with GOLOG implementations. Various situation calculus planners have been implemented. Grounded as our approach is in classical logic, all reasoning and computation rely on first order theorem proving. My talk will focus on how we have succeeded in building efficient implementations, and what are the underlying assumptions that make this possible. For certain applications, for example robotics, some of these assumptions are unrealistic, and I shall describe some of the automated reasoning problems which must be addressed in these settings. For a preview of some of these themes, and the approach taken by the University of Toronto Cognitive Robotics Group, see: http://www.cs.toronto.edu/~cogrobo/