Jürg Kohlas

Bad data analysis for power system state estimation

The state estimation problem in electric power systems consists of four basic operations: hypothesize structure; estimate; detect; identify. This paper addresses the last two problems with respect to the bad data and structural error problem. The paper interrelates various detection and identification methods (sum of squared residuals, weighted and normalized residuals, nonquadratic criteria) and presents new results on bad data analysis (probability of detection, effect of bad data). The theoretical results are illustrated by means of a 25 bus network.

Probabilistic Argumentation Systems

Different formalisms for solving problems of inference under uncertainty have been developed so far. The most popular numerical approach is the theory of Bayesian inference [Lauritzen and Spiegelhalter, 1988]. More general approaches are the Dempster-Shafer theory of evidence [Shafer, 1976], and possibility theory [Dubois and Prade, 1990], which is closely related to fuzzy systems. For these systems computer implementations are available. In competition with these numerical methods are different symbolic approaches. Many of them are based on different types of non-monotonic logic.

Human Machine Interaction

Human Machine Interaction.- Multimodal Interfaces: A Survey of Principles, Models and Frameworks.- Interactive Visualization - A Survey.- Mixed Reality: A Survey.- Multimodal User Interfaces.- Intelligent Multi-modal Interfaces for Mobile Applications in Hostile Environment(IM-HOST).- MEMODULES as Tangible Shortcuts to Multimedia Information.- Why Androids Will Have Emotions: Constructing Human-Like Actors and Communicators Based on Exact Sciences of the Mind.- Interactive Visualization.- EvoSpaces - Multi-dimensional Navigation Spaces for Software Evolution.- HOVISSE - Haptic Osteosynthesis Virtual Intra-operative Surgery Support Environment.- A Language and a Methodology for Prototyping User Interfaces for Control Systems.- Mixed Reality.- See ColOr: Seeing Colours with an Orchestra.- 6 th Sense- Toward a Generic Framework for End-to-End Adaptive Wearable Augmented Reality.

Computation in Valuation Algebras

The main goal of this chapter is to describe an abstract framework called valuation algebra for computing marginals using local computation. The valuation algebra framework is useful in many domains, and especially for managing uncertainty in expert systems using probability, Dempster-Shafer belief functions, Spohnian epistemic belief theory, and possibility theory.

Propositional information systems

Resolution is an often used method for deduction in propositional logic. Here a proper organization of deduction is proposed which avoids redundant computations. It is based on a generic framework of decompositions and local computations as introduced by Shenoy, Shafer [29]. The system contains the two basic operations with information, namely marginalization (or projection) and combination; the latter being an idempotent operation in the present case. The theory permits the conception of an architecture of distributed computing. As an important application assumption-based reasoning is discussed.

Model-based diagnostics and probabilistic assumption-based reasoning

Abstract The mathematical foundations of model-based diagnostics or diagnosis from first principles have been laid by Reiter (1987). In this paper we extend Reiters ideas of model-based diagnostics by introducing probabilities into Reiters framework. This is done in a mathematically sound and precise way which allows one to compute the posterior probability that a certain component is not working correctly given some observations of the system. A straightforward computation of these probabilities is not efficient and in this paper we propose a new method to solve this problem. Our method is logic-based and borrows ideas from assumption-based reasoning and ATMS. We show how it is possible to determine arguments in favor of the hypothesis that a certain group of components is not working correctly. These arguments represent the symbolic or qualitative aspect of the diagnosis process. Then they are used to derive a quantitative or numerical aspect represented by the posterior probabilities. Using two new theorems about the relation between Reiters notion of conflict and our notion of argument, we prove that our so-called degree of support is nothing but the posterior probability that we are looking for. Furthermore, a model where each component may have more than two different operating modes is discussed and a new algorithm to compute posterior probabilities in this case is presented.

Theory of evidence — A survey of its mathematical foundations, applications and computational aspects

The mathematical theory of evidence has been introduced by Glenn Shafer in 1976 as a new approach to the representation of uncertainty. This theory can be represented under several distinct but more or less equivalent forms. Probabilistic interpretations of evidence theory have their roots in Arthur Dempsters multivalued mappings of probability spaces. This leads to random set and more generally to random filter models of evidence. In this probabilistic view evidence is seen as more or less probable arguments for certain hypotheses and they can be used to support those hypotheses to certain degrees. These degrees of support are in fact the reliabilities with which the hypotheses can be derived from the evidence. Alternatively, the mathematical theory of evidence can be founded axiomatically on the notion of belief functions or on the allocation of belief masses to subsets of a frame of discernment. These approaches aim to present evidence theory as an extension of probability theory. Evidence theory has been used to represent uncertainty in expert systems, especially in the domain of diagnostics. It can be applied to decision analysis and it gives a new perspective for statistical analysis. Among its further applications are image processing, project planning and scheduling and risk analysis. The computational problems of evidence theory are well understood and even though the problem is complex, efficient methods are available.

Probabilistic argumentation systems a new way to combine logic with probability

Probability is usually closely related to Boolean structures, i.e., Boolean algebras or propositional logic. Here we show, how probability can be combined with non-Boolean structures, and in particular non-Boolean logics. The basic idea is to describe uncertainty by (Boolean) assumptions, which may or may not be valid. The uncertain information depends then on these uncertain assumptions, scenarios or interpretations. We propose to describe information in information systems, as introduced by Scott into domain theory. This captures a wide range of systems of practical importance such as many propositional logics, first order logic, systems of linear equations, inequalities, etc. It covers thus both symbolic as well as numerical systems. Assumption-based reasoning allows then to deduce supporting arguments for hypotheses. A probability structure imposed on the assumptions permits to quantify the reliability of these supporting arguments and thus to introduce degrees of support for hypotheses. Information systems and related information algebras are formally introduced and studied in this paper as the basic structures for assumption-based reasoning. The probability structure is then formally represented by random variables with values in information algebras. Since these are in general non-Boolean structures some care must be exercised in order to introduce these random variables. It is shown that this theory leads to an extension of Dempster-Shafer theory of evidence and that information algebras provide in fact a natural frame for this theory.

Probabilistic Argumentation Systems and Abduction

Probabilistic argumentation systems are based on assumption-based reasoning for obtaining arguments supporting hypotheses and on probability theory to compute probabilities of supports. Assumption-based reasoning is closely related to hypothetical reasoning or inference through theory formation. The latter approach has well known relations to abduction and default reasoning. In this paper assumption-based reasoning, as an alternative to theory formation aiming at a different goal, will be presented and its use for abduction and model-based diagnostics will be explained. Assumption-based reasoning is well suited for defining a probability structure on top of it. On the base of the relationships between assumption-based reasoning on the one hand and abduction on the other hand, the added value introduced by probability into model based diagnostics will be discussed. Furthermore, the concepts of complete and partial models are introduced with the goal to study the quality of inference procedures. In particular this will be used to compare abductive to possible explanations.

Probabilistic assumption-based reasoning

The classical propositional assumption-based model is extended to incorporate probabilities for the assumptions. Then it is placed into the framework of evidence theory. Several authors like Laskey, Lehner (1989) and Provan (1990) already proposed a similar point of view, but the first paper is not as much concerned with mathematical foundations, and Provans paper develops into a different direction. Here we thoroughly develop and present the mathematical foundations of this theory, together with computational methods adapted from Reiter, De Kleer (1987) and Inoue (1992). Finally, recently proposed techniques for computing degrees of support are presented.