Probabilistic Argumentation and Decision System

The concept of probabilistic argumentation systems PAS is restricted to two types of variables: assumptions, which model the uncertain part of the knowledge, and propositions, which model the rest of the information. Instantiations of PAS have been used for dealing with problems in different contexts. Here, we introduce a third kind of variables into PAS: so-called decision variables. This new kind allows to describe the decisions which a user can make to react on some state of the system. Consider that given a system state, the users can themselves set the values of some decision variables in order to guarantee the requirement. The interesting system states are now those for which the users can find at least one setting of “their” variables under which the requirement imposed on the system can be fulfilled. This can be seen as a game with two players, say nature against a user. Nature makes the first move and the user the second. If the requirement is fulfilled, the user wins (as the system is up), otherwise the user looses. Note that we do not include a concept of utility here as we are only interested in possible settings of decision variables. Further, we present an algorithm for computing arguments which exploits the special structure of PAS with decision variables. This allows now to use this framework for example in model-based reliability theory for computing structure functions.