Possibilistic networks are useful tools for reasoning under uncertainty. Uncertain pieces of information can be described by different measures: possibility measures, necessity measures and more recently, guaranteed possibility measures, denoted by Delta. This paper first proposes the use of guaranteed possibility measures to define a so-called Delta-based possibilistic network. This graphical representation tries to express and to deal with the minimal (lower-bound) possibility degree guaranteed for each variable. We then establish relationships between graphical and logical-based representations of uncertain information encoded by guaranteed possibility measures. We show that possibilistic networks based on guaranteed possibility measures can be easily transformed, in a polynomial time, in Delta-based knowledge bases. Then we analyze propagation algorithms in Delta-based possibilistic networks. In fact, standard possibilistic propagation algorithms can be re-used since we show that a simple rewriting of the chain rule allows the transformation of the initial Delta-based possibilistic networks into standard min-based possibilistic networks.

The Special Track on Uncertain Reasoning (UR) is the oldest FLAIRS special track, running annually since 1996. The UR'09 Special Track at the 2009 FLAIRS Conference is the 14th in the series. UR'09 seeks to bring together researchers working on broad issues related to reasoning under uncertainty. Topics pertaining to the special track included, but were not limited to, uncertain reasoning formalisms, calculi and methodologies; reasoning with probability, possibility, fuzzy logic, belief function, vagueness, granularity, argumentation, rough sets, and probability logics; modeling and reasoning using imprecise and indeterminate information, such as Choquet capacities, comparative orderings, convex sets of measures, and interval-valued probabilities; exact, approximate, and qualitative uncertain reasoning; graphical models of uncertainty; multi-agent uncertain reasoning and decision making; decision-theoretic planning and Markov decision process; temporal reasoning and uncertainty; epistemic logics; nonmonotonic and conditional logics; similarity-based reasoning; construction of models from elicitation, data mining, and knowledge discovery; uncertain reasoning in information retrieval, filtering, fusion, diagnosis, prediction, and situation assessment; and practical applications of uncertain reasoning. Through rigorous reviews by the program committee, UR'09 accepted 9 full papers and 4 posters from 18 submissions, which are included in this proceedings.

In this paper we analyse Belief Propagation over a Gaussian model in a dynamic environment. Recently, this has been proposed as a method to average local measurement values by a distributed protocol ("Consensus Propagation", Moallemi & Van Roy, 2006), where the average is available for read-out at every single node. In the case that the underlying network is constant but the values to be averaged fluctuate ("dynamic data"), convergence and accuracy are determined by the spectral properties of an associated Ruelle-Perron-Frobenius operator. For Gaussian models on Erdos-Renyi graphs, numerical computation points to a spectral gap remaining in the large-size limit, implying exceptionally good scalability. In a model where the underlying network also fluctuates ("dynamic network"), averaging is more effective than in the dynamic data case. Altogether, this implies very good performance of these methods in very large systems, and opens a new field of statistical physics of large (and dynamic) information systems.

A fuzzy mnesor space is a semimodule over the positive real numbers. It can be used as theoretical framework for fuzzy sets. Hence we can prove a great number of properties for fuzzy sets without refering to the membership functions.

In this paper we formulate the problem of inference under incomplete information in very general terms. This includes modelling the process responsible for the incompleteness, which we call the incompleteness process. We allow the process' behaviour to be partly unknown. Then we use Walley's theory of coherent lower previsions, a generalisation of the Bayesian theory to imprecision, to derive the rule to update beliefs under incompleteness that logically follows from our assumptions, and that we call conservative inference rule. This rule has some remarkable properties: it is an abstract rule to update beliefs that can be applied in any situation or domain; it gives us the opportunity to be neither too optimistic nor too pessimistic about the incompleteness process, which is a necessary condition to draw reliable while strong enough conclusions; and it is a coherent rule, in the sense that it cannot lead to inconsistencies. We give examples to show how the new rule can be applied in expert systems, in parametric statistical inference, and in pattern classification, and discuss more generally the view of incompleteness processes defended here as well as some of its consequences.

This paper presents a new method for inferring the semantic properties of documents by leveraging free-text keyphrase annotations. Such annotations are becoming increasingly abundant due to the recent dramatic growth in semi-structured, user-generated online content. One especially relevant domain is product reviews, which are often annotated by their authors with pros/cons keyphrases such as ``a real bargain'' or ``good value.'' These annotations are representative of the underlying semantic properties; however, unlike expert annotations, they are noisy: lay authors may use different labels to denote the same property, and some labels may be missing. To learn using such noisy annotations, we find a hidden paraphrase structure which clusters the keyphrases. The paraphrase structure is linked with a latent topic model of the review texts, enabling the system to predict the properties of unannotated documents and to effectively aggregate the semantic properties of multiple reviews. Our approach is implemented as a hierarchical Bayesian model with joint inference. We find that joint inference increases the robustness of the keyphrase clustering and encourages the latent topics to correlate with semantically meaningful properties. Multiple evaluations demonstrate that our model substantially outperforms alternative approaches for summarizing single and multiple documents into a set of semantically salient keyphrases.

The relationship between Popper spaces (conditional probability spaces that satisfy some regularity conditions), lexicographic probability systems (LPS's), and nonstandard probability spaces (NPS's) is considered. If countable additivity is assumed, Popper spaces and a subclass of LPS's are equivalent; without the assumption of countable additivity, the equivalence no longer holds. If the state space is finite, LPS's are equivalent to NPS's. However, if the state space is infinite, NPS's are shown to be more general than LPS's.

We study the distributions of the LASSO, SCAD, and thresholding estimators, in finite samples and in the large-sample limit. The asymptotic distributions are derived for both the case where the estimators are tuned to perform consistent model selection and for the case where the estimators are tuned to perform conservative model selection. Our findings complement those of Knight and Fu (2000) and Fan and Li (2001). We show that the distributions are typically highly nonnormal regardless of how the estimator is tuned, and that this property persists in large samples. The uniform convergence rate of these estimators is also obtained, and is shown to be slower than 1/root(n) in case the estimator is tuned to perform consistent model selection. An impossibility result regarding estimation of the estimators' distribution function is also provided.

We introduce new definitions of universal and superuniversal computable codes, which are based on a code's ability to approximate Kolmogorov complexity within the prescribed margin for all individual sequences from a given set. Such sets of sequences may be singled out almost surely with respect to certain probability measures. Consider a measure parameterized with a real parameter and put an arbitrary prior on the parameter. The Bayesian measure is the expectation of the parameterized measure with respect to the prior. It appears that a modified Shannon-Fano code for any computable Bayesian measure, which we call the Bayesian code, is superuniversal on a set of parameterized measure-almost all sequences for prior-almost every parameter. According to this result, in the typical setting of mathematical statistics no computable code enjoys redundancy which is ultimately much less than that of the Bayesian code. Thus we introduce another characteristic of computable codes: The catch-up time is the length of data for which the code length drops below the Kolmogorov complexity plus the prescribed margin. Some codes may have smaller catch-up times than Bayesian codes.

An intent expression system using eye robots is proposed for a mascot robot system from a viewpoint of humatronics. The eye robot aims at providing a basic interface method for an information terminal robot system. To achieve better understanding of the displayed information, the importance and the degree of certainty of the information should be communicated along with the main content. The proposed intent expression system aims at conveying this additional information using the eye robot system. Eye motions are represented as the states in a pleasure-arousal space model. Changes in the model state are calculated by fuzzy inference according to the importance and degree of certainty of the displayed information. These changes influence the arousal-sleep coordinates in the space that corresponds to levels of liveliness during communication. The eye robot provides a basic interface for the mascot robot system that is easy to be understood as an information terminal for home environments in a humatronics society.