**Jürg Kohlas & Rolf Haenni**

Probabilistic argumentation systems provide an intuitive and natural approach to non-monotonic reasoning under uncertainty. The basic idea is to find arguments in favor and against certain hypotheses. Arguments are composed of uncertain assumptions, which are used for capturing the uncertainty of the given knowledge. Deriving arguments is a matter of deduction in an appropriate logic. Non-monotonicity is obtained in a natural way by eliminating contradictory arguments.

A quantitative judgement of hypotheses is possible by weighting the uncertain assumptions according to their likelihood or probability. In this way, reliabilities of arguments are obtained and degrees of support and plausibility in the sense of the Dempster-Shafer theory of evidence can be derived for the hypotheses. Probabilistic argumentation systems are therefore based on a novel combination of classical logic (for deduction) and probability theory (for measuring the reliabilities of deductions). The tutorial will present the conceptual foundations of probabilistic argumentation systems. Furthermore, relations to other formalisms (e.g. Bayesian networks, evidence theory, ATMS, probabilistic logic, default logic, etc.) will be elucidated.

The expressiveness of probabilistic argumentation systems permits us to model problems from different domains (e.g. model-based prediction, state estimation and diagnostics, failure trees, project scheduling, sensor fusing, testimonies, public key certification, information retrieval, etc.). This shows its extensive applicability and usefulness for all sorts of problems of reasoning under uncertainty. Several examples of different application fields will be discussed in the tutorial.

Efficient deduction mechanisms are of particular importance for probabilistic argumentation systems. For that purpose, appropriate approximation strategies exist for computing only the most relevant arguments in polynomial time. In this way, the complexity of dealing with logical deduction can be controlled. Based on these considerations, inference mechanisms for probabilistic argumentation systems will be sketched.

**Prerequisite knowledge: **

Only elementary knowledge of propositional logic and discrete
probability is required.

**Prof. Jürg Kohlas**
is professor of theoretical computer science at the University of
Fribourg (Switzerland). He has been a partner of the European Basic
Research Activity "Defeasible Reasoning and Management of Uncertainty"
(1993-1996). He is the leader of the project "Probabilistic
Argumentation Systems" (1997-1999) and the initiator of the project
"Inference and Deduction: an Integration of Logic and Probability",
both sponsored by the Swiss National Foundation for Research.

**Dr. Rolf Haenni**
is research scientist at the Institute of Informatics of the
University of Fribourg. He has been a partner of the European Basic
Research Activity "Defeasible Reasoning and Management of Uncertainty"
(1993-1996), and he is the manager of the project "Probabilistic
Argumentation Systems" (1997-1999).

Both lecturers are experienced in the tutorial topic for many years.

Webmaster: Sven Olofsson, sveno@dsv.su.se Last modified: Mar 16, 1999