The representation of independence relations generally builds upon the well-known semigraphoid axioms of independence. Recently, a representation has been proposed that captures a set of dominant statements of an independence relation from which any other statement can be generated by means of the axioms; the cardinality of this set is taken to indicate the complexity of the relation. Building upon the idea of dominance, we introduce the concept of stability to provide for a more compact representation of independence. We give an associated algorithm for establishing such a representation. We show that, with our concept of stability, many independence relations are found to be of lower complexity than with existing representations.

The logic FO(ID) uses ideas from the field of logic programming to extend first order logic with non-monotone inductive definitions. Such logic formally extends logic programming, abductive logic programming and datalog, and thus formalizes the view on these formalisms as logics of (generalized) inductive definitions. The goal of this paper is to study a deductive inference method for PC(ID), which is the propositional fragment of FO(ID). We introduce a formal proof system based on the sequent calculus (Gentzen-style deductive system) for this logic. As PC(ID) is an integration of classical propositional logic and propositional inductive definitions, our sequent calculus proof system integrates inference rules for propositional calculus and definitions. We present the soundness and completeness of this proof system with respect to a slightly restricted fragment of PC(ID). We also provide some complexity results for PC(ID). By developing the proof system for PC(ID), it helps us to enhance the understanding of proof-theoretic foundations of FO(ID), and therefore to investigate useful proof systems for FO(ID).

This article introduces the benefits of using computer as a tool for foreign language teaching and learning. It describes the effect of using Natural Language Processing (NLP) tools for learning Arabic. The technique explored in this particular case is the employment of pedagogically indexed corpora. This text-based method provides the teacher the advantage of building activities based on texts adapted to a particular pedagogical situation. This paper also presents ARAC: a Platform dedicated to language educators allowing them to create activities within their own pedagogical area of interest.

This paper is an example-based demonstration of our initial results on the formal specification of programs written in the computer algebra language MiniMaple (a substantial subset of Maple with slight extensions). The main goal of this work is to define a verification framework for MiniMaple. Formal specification of MiniMaple programs is rather complex task as it supports non-standard types of objects, e.g. symbols and unevaluated expressions, and additional functions and predicates, e.g. runtime type tests etc. We have used the specification language to specify various computer algebra concepts respective objects of the Maple package DifferenceDifferential developed at our institute.

We single out generalised quantifiers and intensional semantics as areas on which to focus attention for the development of the theory. Once suitable theories have been developed, algorithms will be needed to apply the theory to tasks. Evaluation is a major problem; we single out application to recognising textual entailment and machine translation for this purpose.

An algorithm for pose and motion estimation using corresponding features in images and a digital terrain map is proposed. Using a Digital Terrain (or Digital Elevation) Map (DTM/DEM) as a global reference enables recovering the absolute position and orientation of the camera. In order to do this, the DTM is used to formulate a constraint between corresponding features in two consecutive frames. The utilization of data is shown to improve the robustness and accuracy of the inertial navigation algorithm. Extended Kalman filter was used to combine results of inertial navigation algorithm and proposed vision-based navigation algorithm. The feasibility of this algorithms is established through numerical simulations.

The machine learning community has recently devoted much attention to the problem of inferring causal relationships from statistical data. Most of this work has focused on uncovering connections among scalar random variables. We generalize existing methods to apply to collections of multi-dimensional random vectors, focusing on techniques applicable to linear models. The performance of the resulting algorithms is evaluated and compared in simulations, which show that our methods can, in many cases, provide useful information on causal relationships even for relatively small sample sizes.

We consider the setting of sequential prediction of arbitrary sequences based on specialized experts. We first provide a review of the relevant literature and present two theoretical contributions: a general analysis of the specialist aggregation rule of Freund et al. (1997) and an adaptation of fixed-share rules of Herbster and Warmuth (1998) in this setting. We then apply these rules to the sequential short-term (one-day-ahead) forecasting of electricity consumption; to do so, we consider two data sets, a Slovakian one and a French one, respectively concerned with hourly and half-hourly predictions. We follow a general methodology to perform the stated empirical studies and detail in particular tuning issues of the learning parameters. The introduced aggregation rules demonstrate an improved accuracy on the data sets at hand; the improvements lie in a reduced mean squared error but also in a more robust behavior with respect to large occasional errors.

Consider a weighted or unweighted k-nearest neighbor graph that has been built on n data points drawn randomly according to some density p on R^d. We study the convergence of the shortest path distance in such graphs as the sample size tends to infinity. We prove that for unweighted kNN graphs, this distance converges to an unpleasant distance function on the underlying space whose properties are detrimental to machine learning. We also study the behavior of the shortest path distance in weighted kNN graphs.

Detection and elimination of redundant clauses from propositional formulas in Conjunctive Normal Form (CNF) is a fundamental problem with numerous application domains, including AI, and has been the subject of extensive research. Moreover, a number of recent applications motivated various extensions of this problem. For example, unsatisfiable formulas partitioned into disjoint subsets of clauses (so-called groups) often need to be simplified by removing redundant groups, or may contain redundant variables, rather than clauses. In this report we present a generalized theoretical framework of labelled CNF formulas that unifies various extensions of the redundancy detection and removal problem and allows to derive a number of results that subsume and extend previous work. The follow-up reports contain a number of additional theoretical results and algorithms for various computational problems in the context of the proposed framework.