Preferred Subtheories: An Extended Logical Framework for Default Reasoning

Abstract

We present a general framework for defining nonmonotonic systems based on the notion of preferred maximal consistent subsets of the premises. This framework subsumes David Poole's THEORIST approach to default reasoning as a particular instance. A disadvantage of THEORIST is that it does not allow to represent priorities between defaults adequately (as distinct from blocking defaults in specific situations). We therefore propose two generalizations of Poole's system: in the first generalization several layers of possible hypotheses representing different degrees of reliability are introduced. In a second further generalization a partial ordering between premises is used to distinguish between more and less reliable formulas. In both approaches a formula is provable from a theory if it is possible to construct a consistent argument for it based on the most reliable hypotheses. This allows for a simple representation of priorities between defaults.