Eliminating Unintended Stable Fixpoints for Hybrid Reasoning Systems
This work addresses a limitation in hybrid reasoning systems for AI and knowledge representation, but it appears incremental as it builds on existing AFT theory and focuses on a specific extension.
The paper tackled the problem of defining approximators that utilize information from previous iterations in nonmonotonic semantics, which traditional AFT theory cannot handle, by introducing a methodology similar to AFT that uses priorly computed upper bounds to more precisely capture semantics, and demonstrated its applicability to hybrid MKNF knowledge bases by extending the state-of-the-art approximator.
A wide variety of nonmonotonic semantics can be expressed as approximators defined under AFT (Approximation Fixpoint Theory). Using traditional AFT theory, it is not possible to define approximators that rely on information computed in previous iterations of stable revision. However, this information is rich for semantics that incorporate classical negation into nonmonotonic reasoning. In this work, we introduce a methodology resembling AFT that can utilize priorly computed upper bounds to more precisely capture semantics. We demonstrate our framework's applicability to hybrid MKNF (minimal knowledge and negation as failure) knowledge bases by extending the state-of-the-art approximator.