Local "belief propagation" rules of the sort proposed by Pearl [15] are guaranteed to converge to the correct posterior probabilities in singly connected graphical models. Recently, a number of researchers have empirically demonstrated good performance of "loopy belief propagation" using these same rules on graphs with loops. Perhaps the most dramatic instance is the near Shannon-limit performance of "Turbo codes", whose decoding algorithm is equivalent to loopy belief propagation. Except for the case of graphs with a single loop, there has been little theoretical understanding of the performance of loopy propagation. Here we analyze belief propagation in networks with arbitrary topologies when the nodes in the graph describe jointly Gaussian random variables.

Local "belief propagation" rules of the sort proposed by Pearl [15] are guaranteed to converge to the correct posterior probabilities in singly connected graphical models. Recently, a number of researchers have empirically demonstratedgood performance of "loopy belief propagation" using these same rules on graphs with loops. Perhaps the most dramatic instance is the near Shannon-limit performance of "Turbo codes", whose decoding algorithm is equivalent to loopy belief propagation. Except for the case of graphs with a single loop, there has been little theoretical understandingof the performance of loopy propagation. Here we analyze belief propagation in networks with arbitrary topologies when the nodes in the graph describe jointly Gaussian random variables.

The problem of developing good policies for partially observable Markov decision problems (POMDPs) remains one of the most challenging areas ofresearch in stochastic planning. One line of research in this area involves the use of reinforcement learning with belief states, probability distributionsover the underlying model states. This is a promising methodfor small problems, but its application is limited by the intractability ofcomputing or representing a full belief state for large problems. Recent work shows that, in many settings, we can maintain an approximate belief state, which is fairly close to the true belief state. In particular, great success has been shown with approximate belief states that marginalize out correlations between state variables. In this paper, we investigate two methods of full belief state reinforcement learning and one novel method for reinforcement learning using factored approximate belief states. We compare the performance of these algorithms on several well-known problem from the literature. Our results demonstrate the importance ofapproximate belief state representations for large problems.

We investigate the space efficiency of a Propositional Knowledge Representation (PKR) formalism. Intuitively, the space efficiency of a formalism F in representing a certain piece of knowledge A, is the size of the shortest formula of F that represents A. In this paper we assume that knowledge is either a set of propositional interpretations (models) or a set of propositional formulae (theorems). We provide a formal way of talking about the relative ability of PKR formalisms to compactly represent a set of models or a set of theorems. We introduce two new compactness measures, the corresponding classes, and show that the relative space efficiency of a PKR formalism in representing models/theorems is directly related to such classes. In particular, we consider formalisms for nonmonotonic reasoning, such as circumscription and default logic, as well as belief revision operators and the stable model semantics for logic programs with negation. One interesting result is that formalisms with the same time complexity do not necessarily belong to the same space efficiency class.

The study of belief change has been an active area in philosophy and AI. In recent years two special cases of belief change, belief revision and belief update, have been studied in detail. In a companion paper (Friedman & Halpern, 1997), we introduce a new framework to model belief change. This framework combines temporal and epistemic modalities with a notion of plausibility, allowing us to examine the change of beliefs over time. In this paper, we show how belief revision and belief update can be captured in our framework. This allows us to compare the assumptions made by each method, and to better understand the principles underlying them. In particular, it shows that Katsuno and Mendelzon's notion of belief update (Katsuno & Mendelzon, 1991a) depends on several strong assumptions that may limit its applicability in artificial intelligence. Finally, our analysis allow us to identify a notion of minimal change that underlies a broad range of belief change operations including revision and update.

Starting with a likelihood or preference order on worlds, we extend it to a likelihood ordering on sets of worlds in a natural way, and examine the resulting logic. Lewis earlier considered such a notion of relative likelihood in the context of studying counterfactuals, but he assumed a total preference order on worlds. Complications arise when examining partial orders that are not present for total orders. There are subtleties involving the exact approach to lifting the order on worlds to an order on sets of worlds. In addition, the axiomatization of the logic of relative likelihood in the case of partial orders gives insight into the connection between relative likelihood and default reasoning.

What criteria should be used to select one semantic formalism over another? However, the scope of analyze and gain insight into (that is, models for circumscription, perfect convergence results linking aspects of not just model) such a task. Although much basic problems are NP hard (at best). Ginsberg and Hugh Holbrook work remains to be done, the consensus His point was that just confirming (Stanford University) showed seems to be that there is sufficient that this problem is indeed potentially that default reasoning could be used common ground to warrant serious nasty is not really surprising. Marco Cadoli and as well as to somehow cope with the significant computational advantages.

Truth maintenance is a collection of techniques for doing belief revision. A truth maintenance system's task is to maintain a set of beliefs in such a way that they are not known to be contradictory and no belief is kept without a reason. Truth maintenance systems were introduced in the late seventies by Jon Doyle and in the last five years there has been an explosion of interest in this kind of systems. In this paper we present an annotated bibliography to the literature of truth maintenance systems, grouping the works referenced according to several classifications.

Truth maintenance is a collection of techniques for doing belief revision. A truth maintenance system's task is to maintain a set of beliefs in such a way that they are not known to be contradictory and no belief is kept without a reason. Truth maintenance systems were introduced in the late seventies by Jon Doyle and in the last five years there has been an explosion of interest in this kind of systems. In this paper we present an annotated bibliography to the literature of truth maintenance systems, grouping the works referenced according to several classifications.

Co-winner of The 2005 AAAI Classic Paper Awards. Summary of Significance by Hector Levesque. Proc. AAAI-86