In this paper we show that the problem of deciding the consistency of a knowledge base in the Description Logic ALCM is ExpTime-complete. The M stands for meta-modelling as defined by Motz, Rohrer and Severi. To show our main result, we define an ExpTime Tableau algorithm as an extension of an algorithm for ALC by Nguyen and Szalas.

Probabilistic models with weighted formulas, known as Markov models or log-linear models, are used in many domains. Recent models of weighted orderings between elements that have been proposed as flexible tools to express preferences under uncertainty, are also potentially useful in applications like planning, temporal reasoning, and user modeling. Their computational properties are very different from those of conventional Markov models; because of the transitivity of the “less than” relation, standard methods that exploit structure of the models, such as variable elimination, are not directly applicable, as there are no conditional independencies between the orderings within connected components. The best known algorithms for general inference inthese models are exponential in the number of statements. Here, we present the first algorithms that exploit the available structure. We begin with the special case of models in the form of chains; we present an exact O(n^3) algorithm, where n is the total number of elements. Next, we generalize this technique to models in which the set of statements are comprised of arbitrary sets of atomic weighted preference formulas (while the query and evidence are conjunctions of atomic preference formulas), and the resulting exact algorithm runs in time O(m * n^2 * n^c), where m is the number of preference formulas, n is the number of elements, and c is the maximum number of elements in a linear cut (which depends both on the structure of the model and the order in which the elements are processed)—therefore, this algorithm is tractable for cases in which c can be bounded to a low value. Finally, we report on the results of an empirical evaluation of both algorithms, showing how they scale with reasonably-sized models.

Bisimulation provides structural conditions to characterize indistinguishability between nodes on graph-like structures from an external observer. It is a fundamental notion used in many areas. However, many applications use graphs where nodes have data, and where observers can test for equality or inequality of data values (e.g., asking the attribute "name" of a node to be different from that of all its neighbors). The present work constitutes a first investigation of "data aware"' bisimulations on data graphs. We study the problem of computing such bisimulations, based on the observational indistinguishability for XPath — a language that extends modal logic with tests for data equality. We show that in general the problem is pspace-complete, but identify several restrictions that yield better complexity bounds (coNP, ptime) by controlling suitable parameters of the problem; namely, the amount of em non-locality allowed, and the class of models considered (graph, DAG, tree). In particular, this analysis yields a hierarchy of tractable fragments.

Preference models lie at the core of the formalization for several related notions, such as non-monotonic reasoning,obligations, goals, beliefs, etc. Recently, the interest in integrating dynamic operators in the logics of belief, preference and obligation has gained momentum.This integration sheds light on similarities among several change operations traditionally studied independently of each other. While a prolific approach, important operations, such as the well-known contraction of beliefs or derogation of norms studied in the AGM tradition,have not received proper attention in this framework.In this work, we study codifications of contraction operations, stemming from the work on iterate dbelief change, in the logic of preferences, by means of both semantically defined operations and their counterpart in syntactical priority structures.

This paper is set to study the applicability of AGM-like operations to probabilistic bases. We focus on the problem of consistency restoration, also called consolidation or contraction by falsity. We aim to identify the reasons why the set of AGM postulates based on discrete operations of deletions and accretions is too coarse to treat finely adjustable probabilistic formulas. We propose new principles that allow one to deal with the consolidation of inconsistent probabilistic bases, presenting a finer method called liftable contraction. Furthermore, we show that existing methods for probabilistic consolidation via distance minimization are particular cases of the methods proposed.

The Maximum Inner Product Search (MIPS) problem, prevalent in matrix factorization-based recommender systems, scales linearly with the number of objects to score. Recent work has shown that clever post-processing steps can turn the MIPS problem into a nearest neighbour one, allowing sublinear retrieval time either through Locality Sensitive Hashing or various tree structures that partition the Euclidian space. This work shows that instead of employing post-processing steps, substantially faster retrieval times can be achieved for the same accuracy when inference is not decoupled from the indexing process. By framing matrix factorization to be natively indexable, so that any solution is immediately sublinearly searchable, we use the machinery of Machine Learning to best learn such a solution. We introduce Indexable Probabilistic Matrix Factorization (IPMF) to shift the traditional post-processing complexity into the training phase of the model. Its inference procedure is based on Geodesic Monte Carlo, and adds minimal additional computational cost to standard Monte Carlo methods for matrix factorization. By coupling inference and indexing in this way, we achieve more than a 50% improvement in retrieval time against two state of the art methods, for a given level of accuracy in the recommendations of two large-scale recommender systems.

A construct that has been receiving attention recently in reinforcement learning is stochastic factorization (SF), a particular case of non-negative factorization (NMF) in which the matrices involved are stochastic. The idea is to use SF to approximate the transition matrices of a Markov decision process (MDP). This is useful for two reasons. First, learning the factors of the SF instead of the transition matrices can reduce significantly the number of parameters to be estimated. Second, it has been shown that SF can be used to reduce the number of operations needed to compute an MDP's value function. Recently, an algorithm called expectation-maximization SF (EMSF) has been proposed to compute a SF directly from transitions sampled from an MDP. In this paper we take a closer look at EMSF. First, by exploiting the assumptions underlying the algorithm, we show that it is possible to reduce it to simple multiplicative update rules similar to the ones that helped popularize NMF. Second, we analyze the optimization process underlying EMSF and find that it minimizes a modified version of the Kullback-Leibler divergence that is particularly well-suited for learning a SF from data sampled from an arbitrary distribution. Third, we build on this improved understanding of EMSF to draw an interesting connection with NMF and probabilistic latent semantic analysis. We also exploit the simplified update rules to introduce a new version of EMSF that generalizes and significantly improves its precursor. This new algorithm provides a practical mechanism to control the trade-off between memory usage and computing time, essentially freeing the space complexity of EMSF from its dependency on the number of sample transitions. The algorithm can also compute its approximation incrementally, which makes it possible to use it concomitantly with the collection of data. This feature makes the new version of EMSF particularly suitable for online reinforcement learning. Empirical results support the utility of the proposed algorithm.

We study the complexity of exchanging probabilistic data between ontology-based probabilistic databases. We consider the Datalog+/- family of languages as ontology and ontology mapping languages, and we assume different compact encodings of the probabilities of the probabilistic source databases via Boolean events. We provide an extensive complexity analysis of the problem of deciding the existence of a probabilistic (universal) solution for a given probabilistic source database relative to a (probabilistic) data exchange problem for the different languages considered.

Over the past two decades, water markets have been successfully fielded in countries such as Australia, the United states, Chile, China, etc. Water users, mainly irrigators, have benefited immensely from water markets. However, the current water market design also faces certain serious barriers. It has been pointed out that transaction costs, which exists in most markets, induce great welfare loss. For example, for water markets in western China discussed in this paper, the influence of transaction costs is significant. Another important barrier is the locality of trades due to geographical constraints. Based on the water market at Xiying Irrigation, one of the most successful water market in western China, we model the water market as a graph with minimum transaction thresholds on edges. Our goal is to maximize the transaction volume or welfare. We prove that the existence of transaction costs results in no polynomial time approximation scheme (PTAS) to maximize social welfare (MAX SNP-hard). The complexities on special graphs are also presented. From a practical point of view, however, optimal social welfare can be obtained via a well-designed mixed integer linear program and can be approximated near optimally at a large scale via a heuristic algorithm. Both algorithms are tested on data sets generated from real historical trading data. Our study also suggests the importance of reducing transaction costs, for example, institutional costs in water market design. Our work opens a potentially important avenue of market design within the agenda of computational sustainability.

Jody Williams received the Nobel Peace Prize in 1997 together with the International Campaign to Ban Landmines for their central role in establishing the 1997 Mine Ban Treaty. The US-based political activist is known across the world for her efforts to enhance understandings of security and related issues in the world today. She is also the chair of the Noble Women's Initiative that she founded in 2006 together with five other women Nobel Peace laureates. She, along with 20 of her fellow Nobel Peace laureates have called for a preemptive ban on Lethal Autonomous Weapons Systems (LAWS)--weapons that could operate without human supervision once activated even in matters of killing human beings. The UN's Convention on Certain Conventional Weapons (CCW) held their third informal government's meet in Geneva from 11-15 April.