Abstract

This dissertation discusses different phenomena all belonging to the wider topic of "uncertainty handling." Each of the following three essays will attempt to discuss approaches that allow a particular uncertainty phenomenon to be introduced into a symbolic reasoning process. The presentation of such approaches will be embedded in the context of symbolic logic and emphasis will be placed on providing not only an inferential mechanism for allowing reasoning to proceed in the presence of the particular uncertainty phenomenon, but also to establish a semantical understanding of the mechanism involved. The first essay will investigate the applicability of the resolution principle to reasoning within the framework of fuzzy logic. We will present a new approach which, while subsuming previously suggested alternatives, is not subject to restrictions imposed on those. Nonmonotonic logic is intended to apply specifically to situations where the initial information is incomplete. In the second essay we will describe a nonmonotonic logic for the Herbrand subset of first-order predicate logic. This nonmonotonic logic will be shown to be both sound and complete. Nonmonotonic logic has been proposed as a solution to vexing problems for knowledge representation. Much debate arose recently around the claim that nonmonotonic logic has to rely on reasoning about generated models. In the third essay we will examine and reject various criteria which have been put forward to determine correct models, and develop a preference criterion between models of our own