Sequential Thresholds: Context Sensitive Default Extensions
This work addresses a foundational problem in non-monotonic reasoning for AI and logic communities, offering an incremental improvement by integrating context sensitivity.
The paper tackles the conceptual difficulties of default logic in representing common sense reasoning by proposing sequential thresholding as a quantitative counterpart that explicitly incorporates evolving context, linking it with default logic to provide a semantic characterization and integration method.
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.