Eliminating Unintended Stable Fixpoints for Hybrid Reasoning Systems

TL;DR

This paper introduces a novel methodology that enhances hybrid reasoning systems by utilizing prior information to eliminate unintended stable fixpoints, thereby improving semantic precision in nonmonotonic reasoning with classical negation.

Contribution

It extends Approximation Fixpoint Theory to incorporate prior iteration information, enabling more accurate semantics in hybrid MKNF knowledge bases.

Findings

Enhanced approximator for hybrid MKNF semantics

More precise capture of nonmonotonic reasoning semantics

Demonstrated applicability to complex knowledge bases

Abstract

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.