Unifying Practical Uncertainty Representations: II. Clouds

There exist many simple tools for jointly capturing variability and incomplete information by means of uncertainty representations. Among them are random sets, possibility distributions, probability intervals, and the more recent Ferson's p-boxes and Neumaier's clouds, both defined by pairs of possibility distributions. In the companion paper, we have extensively studied a generalized form of p-box and situated it with respect to other models . This paper focuses on the links between clouds and other representations. Generalized p-boxes are shown to be clouds with comonotonic distributions. In general, clouds cannot always be represented by random sets, in fact not even by 2-monotone (convex) capacities.Comment: 30 pages, 7 figures, Pre-print of journal paper to be published in International Journal of Approximate Reasoning (with expanded section concerning clouds and probability intervals

Degenerate Gaussian factors for probabilistic inference

In this paper, we propose a parametrised factor that enables inference on Gaussian networks where linear dependencies exist among the random variables. Our factor representation is effectively a generalisation of traditional Gaussian parametrisations where the positive-definite constraint of the covariance matrix has been relaxed. For this purpose, we derive various statistical operations and results (such as marginalisation, multiplication and affine transformations of random variables) that extend the capabilities of Gaussian factors to these degenerate settings. By using this principled factor definition, degeneracies can be accommodated accurately and automatically at little additional computational cost. As illustration, we apply our methodology to a representative example involving recursive state estimation of cooperative mobile robots.Comment: Accepted by International Journal of Approximate Reasoning on 17 January 202

Binary Join Trees

A longer and updated version of this paper appears in: Shenoy, P. P., "Binary Join Trees for Computing Marginals in the Shenoy-Shafer Architecture," International Journal of Approximate Reasoning, 17(2--3), 1997, 239--263 (available from .The main goal of this paper is to describe a datastructure called binary join trees that are useful incomputing multiple marginals efficiently usingthe Shenoy-Shafer architecture. We define binaryjoin trees, describe their utility, and sketch a procedure for constructing them

Reasoning about norms under uncertainty in dynamic environments

The behaviour of norm-autonomous agents is determined by their goals and the norms that are explicitly represented inside their minds. Thus, they require mechanisms for acquiring and accepting norms, determining when norms are relevant to their case, and making decisions about norm compliance. Up un- til now the existing proposals on norm-autonomous agents assume that agents interact within a deterministic environment that is certainly perceived. In prac- tice, agents interact by means of sensors and actuators under uncertainty with non-deterministic and dynamic environments. Therefore, the existing propos- als are unsuitable or, even, useless to be applied when agents have a physical presence in some real-world environment. In response to this problem we have developed the n-BDI architecture. In this paper, we propose a multi -context graded BDI architecture (called n-BDI) that models norm-autonomous agents able to deal with uncertainty in dynamic environments. The n-BDI architecture has been experimentally evaluated and the results are shown in this paper.This paper was partially funded by the Spanish government under Grant CONSOLIDER-INGENIO 2010 CSD2007-00022 and the Valencian government under Project PROMETEOH/2013/019.Criado Pacheco, N.; Argente, E.; Noriega, P.; Botti Navarro, VJ. (2014). Reasoning about norms under uncertainty in dynamic environments. International Journal of Approximate Reasoning. 55(9):2049-2070. https://doi.org/10.1016/j.ijar.2014.02.004S2049207055