Among the many approaches for reasoning about degrees of belief in the presence of noisy sensing and acting, the logical account proposed by Bacchus, Halpern, and Levesque is perhaps the most expressive. While their formalism is quite general, it is restricted to fluents whose values are drawn from discrete finite domains, as opposed to the continuous domains seen in many robotic applications. In this work, we show how this limitation in that approach can be lifted. By dealing seamlessly with both discrete distributions and continuous densities within a rich theory of action, we provide a very general logical specification of how belief should change after acting and sensing in complex noisy domains.
 This paper extends earlier work by its authors on formal aspects of the processes of contracting a theory to eliminate a proposition and revising a theory to introduce a proposition. In the course of the earlier work, Gardenfors developed general postulates of a more or less equational nature for such processes, whilst Alchourron and Makinson studied the particular case of contraction functions that are maximal, in the sense of yielding a maximal subset of the theory (or alternatively, of one of its axiomatic bases), that fails to imply the proposition being eliminated. In the present paper, the authors study a broader class, including contraction functions that may be less than maximal. Specifically, they investigate “partial meet contraction functions”, which are defined to yield the intersection of some nonempty family of maximal subsets of the theory that fail to imply the proposition being eliminated. Basic properties of these functions are established: it is shown in particular that they satisfy the Gardenfors postulates, and moreover that they are sufficiently general to provide a representation theorem for those postulates. Some special classes of partial meet contraction functions, notably those that are “relational” and “transitively relational”, are studied in detail, and their connections with certain “supplementary postulates” of Gardenfors investigated, with a further representation theorem established. This paper develops a declarative language, P-log, that combines logical and probabilistic arguments in its reasoning. Answer Set Prolog is used as the logical foundation, while causal Bayes nets serve as a probabilistic foundation. We give several non-trivial examples and illustrate the use of P-log for knowledge representation and updating of knowledge. We argue that our approach to updates is more appealing than existing approaches. We give sufficiency conditions for the coherency of P-log programs and show that Bayes nets can be easily mapped to coherent P-log programs. According to the paradigm of Cognitive Robotics (Reiter, 2001a), intelligent, autonomous agents interacting with an incompletely known world need to reason logically about the effects of their actions and sensor information they acquire over time. In realistic settings, both the effect of actions and sensor data are subject to errors. A cognitive agent can cope with these uncertainties by maintaining probabilistic beliefs about the state of world. In this paper, we show a formalism to represent probabilistic beliefs about states of the world and how these beliefs change in the course of actions. Additionally, we propose an extension to a logic programming framework, the agent programming language FLUX, to actually infer this probabilistic knowledge for agents. Using associated Bayesian networks allows the agents to maintain a single and compact probabilistic knowledge state throughout the execution of an action sequence.  John McCarthy's situation calculus has left an enduring mark on artificial intelligence research. This simple yet elegant formalism for modelling and reasoning about dynamic systems is still in common use more than forty years since it was first proposed. The ability to reason about action and change has long been considered a necessary component for any intelligent system. The situation calculus and its numerous extensions as well as the many competing proposals that it has inspired deal with this problem to some extent. In this paper, we offer a new approach to belief change associated with performing actions that addresses some of the shortcomings of these approaches. In particular, our approach is based on a well-developed theory of action in the situation calculus extended to deal with belief. Moreover, by augmenting this approach with a notion of plausibility over situations, our account handles nested belief, belief introspection, mistaken belief, and handles belief revision and belief update together with iterated belief change. This paper proposes a method for handling the frame problem for knowledge-producing actions. An example of a knowledge-producing action is a sensing operation performed by a robot to determine whether or not there is an object of a particular shape within its grasp. The work is an extension of Reiter's approach to the frame problem for ordinary actions and Moore's work on knowledge and action. The properties of our specification are that knowledge-producing actions do not affect fluents other than the knowledge fluent, and actions that are not knowledge-producing only affect the knowledge fluent as appropriate. In addition, memory emerges as a side-effect: if something is known in a certain situation, it remains known at successor situations, unless something relevant has changed. Also, it will be shown that a form of regression examined by Reiter for reducing reasoning about future situations to reasoning about the initial situation now also applies to knowledge-producing actions. Ignoring the noise of physical sensors and effectors has always been a crucial barrier towards the application of high-level, cognitive robotics to real robots. We present a method of solving planning problems with noisy actions. The approach builds on the Fluent Calculus as a standard first-order solution to the Frame Problem. To model noise, a formal notion of uncertainty is incorporated into the axiomatization of state update and knowledge update. The formalism provides the theoretical underpinnings of an extension of the action programming language Flux. Using constraints on real-valued intervals to encode noise, our system allows to solve planning problems for noisy sensors and effectors.