We look at the problem of revising fuzzy belief bases, i.e., belief base revision in which both formulas in the base as well as revision-input formulas can come attached with varying truth-degrees. Working within a very general framework for fuzzy logic which is able to capture a variety of types of inference under uncertainty, such as truth-functional fuzzy logics and certain types of probabilistic inference, we show how the idea of rational change from 'crisp' base revision, as embodied by the idea of partial meet revision, can be faithfully extended to revising fuzzy belief bases. We present and axiomatise an operation of partial meet fuzzy revision and illustrate how the operation works in several important special instances of the framework.

For a given problem, the optimal Markov policy can be considerred as a conditional or contingent plan containing a (potentially large) number of branches. Unfortunately, there are applications where it is desirable to strictly limit the number of decision points and branches in a plan. For example, it may be that plans must later undergo more detailed simulation to verify correctness and safety, or that they must be simple enough to be understood and analyzed by humans. As a result, it may be necessary to limit consideration to plans with only a small number of branches. This raises the question of how one goes about finding optimal plans containing only a limited number of branches. In this paper, we present an any-time algorithm for optimal k-contingency planning (OKP). It is the first optimal algorithm for limited contingency planning that is not an explicit enumeration of possible contingent plans. By modelling the problem as a Partially Observable Markov Decision Process, it implements the Bellman optimality principle and prunes the solution space. We present experimental results of applying this algorithm to some simple test cases.

We present CLP(BN), a novel approach that aims at expressing Bayesian networks through the constraint logic programming framework. Arguably, an important limitation of traditional Bayesian networks is that they are propositional, and thus cannot represent relations between multiple similar objects in multiple contexts. Several researchers have thus proposed first-order languages to describe such networks. Namely, one very successful example of this approach are the Probabilistic Relational Models (PRMs), that combine Bayesian networks with relational database technology. The key difficulty that we had to address when designing CLP(cal{BN}) is that logic based representations use ground terms to denote objects. With probabilitic data, we need to be able to uniquely represent an object whose value we are not sure about. We use {sl Skolem functions} as unique new symbols that uniquely represent objects with unknown value. The semantics of CLP(cal{BN}) programs then naturally follow from the general framework of constraint logic programming, as applied to a specific domain where we have probabilistic data. This paper introduces and defines CLP(cal{BN}), and it describes an implementation and initial experiments. The paper also shows how CLP(cal{BN}) relates to Probabilistic Relational Models (PRMs), Ngo and Haddawys Probabilistic Logic Programs, AND Kersting AND De Raedts Bayesian Logic Programs.

The paper studies empirically the time-space trade-off between sampling and inference in a sl cutset sampling algorithm. The algorithm samples over a subset of nodes in a Bayesian network and applies exact inference over the rest. Consequently, while the size of the sampling space decreases, requiring less samples for convergence, the time for generating each single sample increases. The w-cutset sampling selects a sampling set such that the induced-width of the network when the sampling set is observed is bounded by w, thus requiring inference whose complexity is exponential in w. In this paper, we investigate performance of w-cutset sampling over a range of w values and measure the accuracy of w-cutset sampling as a function of w. Our experiments demonstrate that the cutset sampling idea is quite powerful showing that an optimal balance between inference and sampling benefits substantially from restricting the cutset size, even at the cost of more complex inference.

Loopy and generalized belief propagation are popular algorithms for approximate inference in Markov random fields and Bayesian networks. Fixed points of these algorithms correspond to extrema of the Bethe and Kikuchi free energy. However, belief propagation does not always converge, which explains the need for approaches that explicitly minimize the Kikuchi/Bethe free energy, such as CCCP and UPS. Here we describe a class of algorithms that solves this typically nonconvex constrained minimization of the Kikuchi free energy through a sequence of convex constrained minimizations of upper bounds on the Kikuchi free energy. Intuitively one would expect tighter bounds to lead to faster algorithms, which is indeed convincingly demonstrated in our simulations. Several ideas are applied to obtain tight convex bounds that yield dramatic speed-ups over CCCP.

We present an application of hierarchical Bayesian estimation to robot map building. The revisiting problem occurs when a robot has to decide whether it is seeing a previously-built portion of a map, or is exploring new territory. This is a difficult decision problem, requiring the probability of being outside of the current known map. To estimate this probability, we model the structure of a "typical" environment as a hidden Markov model that generates sequences of views observed by a robot navigating through the environment. A Dirichlet prior over structural models is learned from previously explored environments. Whenever a robot explores a new environment, the posterior over the model is estimated by Dirichlet hyperparameters. Our approach is implemented and tested in the context of multi-robot map merging, a particularly difficult instance of the revisiting problem. Experiments with robot data show that the technique yields strong improvements over alternative methods.

Inferences in directed acyclic graphs associated with probability sets and probability intervals are NP-hard, even for polytrees. In this paper we focus on such inferences, and propose: 1) a substantial improvement on Tessems A / R algorithm FOR polytrees WITH probability intervals; 2) a new algorithm FOR direction - based local search(IN sets OF probability) that improves ON existing methods; 3) a collection OF branch - AND - bound algorithms that combine the previous techniques.The first two techniques lead TO approximate solutions, WHILE branch - AND - bound procedures can produce either exact OR approximate solutions.We report ON dramatic improvements ON existing techniques FOR inference WITH probability sets AND intervals, IN SOME cases reducing the computational effort BY many orders OF magnitude.

By elaborating on the notion of linear belief functions (Dempster 1990; Liu 1996), we propose an elementary approach to knowledge representation for expert systems using linear belief functions. We show how to use basic matrices to represent market information and financial knowledge, including complete ignorance, statistical observations, subjective speculations, distributional assumptions, linear relations, and empirical asset pricing models. We then appeal to Dempster's rule of combination to integrate the knowledge for assessing an overall belief of portfolio performance, and updating the belief by incorporating additional information. We use an example of three gold stocks to illustrate the approach.

This paper presents a scalable Bayesian technique for decentralized state estimation from multiple platforms in dynamic environments. As has long been recognized, centralized architectures impose severe scaling limitations for distributed systems due to the enormous communication overheads. We propose a strictly decentralized approach in which only nearby platforms exchange information. They do so through an interactive communication protocol aimed at maximizing information flow. Our approach is evaluated in the context of a distributed surveillance scenario that arises in a robotic system for playing the game of laser tag. Our results, both from simulation and using physical robots, illustrate an unprecedented scaling capability to large teams of vehicles.

In a standard possibilistic logic, prioritized information are encoded by means of weighted knowledge base. This paper proposes an extension of possibilistic logic for dealing with partially ordered information. We Show that all basic notions of standard possibilitic logic (sumbsumption, syntactic and semantic inference, etc.) have natural couterparts when dealing with partially ordered information. We also propose an algorithm which computes possibilistic conclusions of a partial knowledge base of a partially ordered knowlege base.