Norbert Lehmann

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.

Resource bounded and anytime approximation of belief function computations

Abstract This paper proposes a new approximation method for Dempster–Shafer belief functions. The method is based on a new concept of incomplete belief potentials. It allows to compute simultaneously lower and upper bounds for belief and plausibility. Furthermore, it can be used for a resource-bounded propagation scheme, in which the user determines in advance the maximal time available for the computation. This leads then to convenient, interruptible anytime algorithms giving progressively better solutions as execution time goes on, thus offering to trade the quality of results against the costs of computation. The paper demonstrates the usefulness of these new methods and shows its advantages and drawbacks compared to existing techniques.

Probabilistic argumentation systems: a new perspective on the dempster-shafer theory

The goal of this article is to study the connection between the Dempster‐Shafter theory (DST) and probabilistic argumentation systems (PASs). By introducing a general method to translate PASs into corresponding Dempster‐Shafter belief potentials, its contribution is twofold. On the one hand, the article proposes PASs as a convenient and powerful modeling language to be put on top of the DST. On the other hand, it shows how to use the DST as an efficient computational tool for numerical computations in PASs.

Implementing Belief Function Computations

This article discusses several implementation aspects for Dempster‐Shafer belief functions. The main objective is to propose an appropriate representation of mass functions and efficient data structures and algorithms for the two basic operations of combination and marginalization.

Assumption-Based Modeling Using ABEL

Today, different formalisms exist to solve reasoning problems under uncertainty. For most of the known formalisms, corresponding computer implementations are available. The problem is that each of the existing systems has its own user interface and an individual language to model the knowledge and the queries.

An Alternative to Outward Propagation for Dempster-Shafer Belief Functions

Given several Dempster-Shafer belief functions, the framework of valuation networks describes an efficient method for computing the marginal of the combined belief function. The computation is based on a message passing scheme in a Markov tree where after the selection of a root node an inward and an outward propagation can be distinguished. In this paper it will be shown that outward propagation can be replaced by another partial inward propagation. In addition it will also be shown how the efficiency of inward propagation can be improved.

Fast-Division Architecture for Dempster-Shafer Belief Functions

Given a number of Dempster-Shafer belief functions there are different architectures which allow to do a compilation of the given knowledge. These architectures are the Shenoy-Shafer Architecture, the Lauritzen-Spiegelhalter Architecture and the HUGIN Architecture. We propose a new architecture called “Fast-Division Architecture” which is similar to the former two. But there are two important advantages: (i) results of intermediate computations are always valid Dempster-Shafer belief functions and (ii) some operations can often be performed much more efficiently.

ABEL: An interactive tool for probabilistic argumentative reasoning

Most formal approaches to argumentative reasoning under uncertainty focus on the analysis of qualitative aspects. An exception is the framework of probabilistic argumentation systems. Its philosophy is to include both qualitative and quantitative aspects through a simple way of combining logic and probability theory. Probabilities are used to weigh arguments for and against particular hypotheses. ABEL is a language that allows to describe probabilistic argumentation systems and corresponding queries about hypotheses. It then returns arguments and counter-arguments with corresponding numerical weights.

Model-Based Diagnostics Using Hints

It is often possible to describe the correct functioning of a system by a mathematical model. As long as observations or measurements correspond to the predictions made by the model, the system may be assumed to be functioning correctly. When, however, a discrepancy arises between the observations and the model-based predictions, then an explanation for this fact has to be found. The foundation of this approach to diagnostics has been laid by Reiter (1987). The explanations generated by his method, called diagnoses, are not unique in general. In addition, they are not weighed by a likelihood measure which would make it possible to compare them. We propose here the theory of hints — an interpretation of the Dempster-Shafer Theory of Evidence — as a very natural and general method for model-based diagnostics (for an introduction to the theory of hints, see (Kohlas & Monney, 1995)). Note that (Peng & Reggia, 1990) and (DeKleer & Williams, 1987) also discuss probabilistic approaches to diagnostic problems.

Building Argumentation Systems on Set Constraint Logic

The purpose of this paper is to show how the theory of probabilistic argumentation systems can be extended from propositional logic to the more general framework of set constraint logic. The strength of set constraint logic is that logical relations between non-binary variables can be expressed more directly. This simplifies the classical way of modeling knowledge through propositional logic. Building argumentation systems on set constraint logic is therefore useful for improving its capabilities of expressing different forms of uncertain knowledge.