Sequential Thresholds: Context Sensitive Default Extensions

Abstract: Default logic encounters some conceptual difficulties in representing common sense reasoning tasks. We argue that we should not try to formulate modular default rules that are presumed to work in all or most circumstances. We need to take into account the importance of the context which is continuously evolving during the reasoning process. Sequential thresholding is a quantitative counterpart of default logic which makes explicit the role context plays in the construction of a non-monotonic extension. We present a semantic characterization of generic non-monotonic reasoning, as well as the instantiations pertaining to default logic and sequential thresholding. This provides a link between the two mechanisms as well as a way to integrate the two that can be beneficial to both.