Probabilistic Assumption-Based Reasoning

Abstract

In Chap. 1, sections 1.1 to 1.3 it has been shown that it is possible to represent uncertain information and uncertain knowledge by uncertain rules or — alternatively — by rules containing uncertain or only probable assumptions. Propositional systems containing uncertain assumptions provide a concise language for describing uncertain information and knowledge. They allow for efficient inference mechanisms based on well known methods from logic and from reliability theory. That is why they are of great interest. In this chapter the relevant methods and techniques will be developed and illustrated. It will be shown how propositional systems with uncertain assumptions fit into the framework of the theory of hints. It turns out that the point of view developed in this chapter is especially well suited to illustrate the basic philosophy of the theory of hints as a logic of reliable reasoning with unreliable arguments.