We introduce the problem of PAC rank elicitation, which consists of sorting a given set of options based on adaptive sampling of stochastic pairwise preferences. More specifically, we assume the existence of a ranking procedure, such as Copeland's method, that determines an underlying target order of the options. The goal is to predict a ranking that is sufficiently close to this target order with high probability, where closeness is measured in terms of a suitable distance measure. We instantiate this setting with combinations of two different distance measures and ranking procedures. For these instantiations, we devise efficient strategies for sampling pairwise preferences and analyze the corresponding sample complexity. We also present first experiments to illustrate the practical performance of our methods.

We study the problem of rewriting a disjunctive datalog program into plain datalog. We show that a disjunctive program is rewritable if and only if it is equivalent to a linear disjunctive program, thus providing a novel characterisation of datalog rewritability. Motivated by this result, we propose weakly linear disjunctive datalog -- a novel rule-based KR language that extends both datalog and linear disjunctive datalog and for which reasoning is tractable in data complexity. We then explore applications of weakly linear programs to ontology reasoning and propose a tractable extension of OWL 2 RL with disjunctive axioms. Our empirical results suggest that many non-Horn ontologies can be reduced to weakly linear programs and that query answering over such ontologies using a datalog engine is feasible in practice.

Various representations and inference methods have been proposed for lifted probabilistic inference in relational models. Many of these methods choose an order to eliminate (or branch on) the parameterized random variables. Similar to such methods for non-relational probabilistic inference, the order of elimination has a significant role in the performance of the algorithms. Since finding the best order is NP-complete even for non-relational models, heuristics have been proposed to find good orderings in the non-relational models. In this paper, we show that these heuristics are inefficient for relational models, because they fail to consider the population sizes associated with logical variables. We extend existing heuristics for non-relational models and propose new heuristics for relational models. We evaluate the existing and new heuristics on a range of generated relational graphs.

In this paper we consider the setting of graph-structured data that evolves as a result of operations carried out by users or applications. We study different reasoning problems, which range from ensuring the satisfaction of a given set of integrity constraints after a given sequence of updates, to deciding the (non-)existence of a sequence of actions that would take the data to an (un)desirable state, starting either from a specific data instance or from an incomplete description of it. We consider a simple action language in which actions are finite sequences of insertions and deletions of nodes and labels, and use Description Logics for describing integrity constraints and (partial) states of the data. We then formalize the data management problems mentioned above as a static verification problem and several planning problems. We provide algorithms and tight complexity bounds for the formalized problems, both for an expressive DL and for a variant of DL-Lite.

Recent work introduced Generalized First Order Decision Diagrams (GFODD) as a knowledge representation that is useful in mechanizing decision theoretic planning in relational domains. GFODDs generalize function-free first order logic and include numerical values and numerical generalizations of existential and universal quantification. Previous work presented heuristic inference algorithms for GFODDs. In this paper, we study the complexity of the evaluation problem, the satiability problem, and the equivalence problem for GFODDs under the assumption that the size of the intended model is given with the problem, a restriction that guarantees decidability. Our results provide a complete characterization. The same characterization applies to the corresponding restriction of problems in first order logic, giving an interesting new avenue for efficient inference when the number of objects is bounded. Our results show that for Σk formulas, and for corresponding GFODDs, evaluation and satisfiability are Σkp complete, and equivalence is Πk+1p complete. For Πk formulas evaluation is Πkp complete, satisfiability is one level higher and is Σk+1p complete, and equivalence is Πk+1p complete.

We present a novel approach to parallel materialisation (i.e., fixpoint computation) of datalog programs in centralised, main-memory, multi-core RDF systems. Our approach comprises an algorithm that evenly distributes the workload to cores, and an RDF indexing data structure that supports efficient, 'mostly' lock-free parallel updates. Our empirical evaluation shows that our approach parallelises computation very well: with 16 physical cores, materialisation can be up to 13.9 times faster than with just one core.

Dung's argumentation framework is an abstract framework based on a set of arguments and a binary attack relation defined over the set. One instantiation, among many others, of Dung's framework consists in constructing the arguments from a set of propositional logic formulas. Thus an argument is seen as a reason for or against the truth of a particular statement. Despite its advantages, the argumentation approach for inconsistency handling also has important shortcomings. More precisely, in some applications what one is interested in are not so much only the conclusions supported by the arguments but also the precise explications of such conclusions. We show that argumentation framework applied to classical logic formulas is not suitable to deal with this problem. On the other hand, intuitionistic logic appears to be a natural alternative candidate logic (instead of classical logic) to instantiate Dung's framework. We develop constructive argumentation framework. We show that intuitionistic logic offers nice and desirable properties of the arguments. We also provide a characterization of the arguments in this setting in terms of minimal inconsistent subsets when intuitionistic logic is embedded in the modal logic S4.

In disease mapping, the spatial scan statistic is used to detect spatial regions where population is exposed to a significantly higher disease risk than expected. In this important application, the current residence is typically used to define the location of individuals from the population. Considering the mobility of humans at various temporal and spatial scales, using only information about the current residence may be an insufficiently informative proxy because it ignores a multitude of exposures that may occur away from home, or which had occurred at previous residences. In this paper, we propose a spatial scan statistic that is appropriate for disease mapping on mobile populations. We formulate a computationally efficient algorithm that uses the proposed statistic to find significant high-risk regions from mobile population's disease status data. The algorithm is applicable on large populations and over dense spatial grids. The experimental results demonstrate that the proposed algorithm is computationally efficient and outperforms the traditional disease clustering approaches at discovering high-risk regions in mobile populations.

Tensor completion is an important topic in the area of image processing and computer vision research, which is generally built on extraction of the intrinsic structure of the tensor data. Drawing on this fact, action classification, relying heavily on the extracted features of high-dimensional tensors, may indeed benefit from tensor completion techniques. In this paper, we propose a low-rank tensor completion method for action classification, as well as image recovery. Since there may exist distortion and corruption in the tensor representations of video sequences, we project the tensors into a subspace, which contains the invariant structure of the tensors. In order to integrate useful supervisory information for classification, we adopt a discriminant analysis criterion to learn the projection matrices. The resulting multi-variate optimization problem can be effectively solved using the augmented Lagrange multiplier (ALM) algorithm. Experiments demonstrate that our method results with better accuracy compared with some other state-of-the-art low-rank tensor representation learning approaches on the MSR Hand Gesture 3D database and the MSR Action 3D database. By denoising the Multi-PIE face database, our experimental setup testifies the proposed method can also be employed to recover images.

The Fisher market model is one of the most fundamental resource allocation models in economics. In a Fisher market, the prices and allocations of goods are determined according to the preferences and budgets of buyers to clear the market. In a Fisher market game, however, buyers are strategic and report their preferences over goods; the market-clearing prices and allocations are then determined based on their reported preferences rather than their real preferences. We show that the Fisher market game always has a pure Nash equilibrium, for buyers with linear, Leontief, and Cobb-Douglas utility functions, which are three representative classes of utility functions in the important Constant Elasticity of Substitution (CES) family. Furthermore, to quantify the social efficiency, we prove Price of Anarchy bounds for the game when the utility functions of buyers fall into these three classes respectively.