Propositional Abduction via Only-Knowing: A Non-Monotonic Approach

TL;DR

This paper presents a non-monotonic logic framework for propositional abduction based on only-knowing, integrating modal operators and preferential relations to model abductive reasoning and explanation selection.

Contribution

It introduces a novel modal logic of knowledge and abduction extending Levesque's only-knowing, with a non-monotonic extension for explanation selection.

Findings

Provides a formal non-monotonic logic for abduction

Establishes properties of the non-monotonic consequence relations

Demonstrates the framework's ability to model explanation selection methods

Abstract

The paper introduces a basic logic of knowledge and abduction by extending Levesque logic of only-knowing with an abduction modal operator defined via the combination of basic epistemic concepts. The upshot is an alternative approach to abduction that employs a modal vocabulary and explores the relation between abductive reasoning and epistemic states of only knowing. Furthermore, by incorporating a preferential relation into modal frames, we provide a non-monotonic extension of our basic framework capable of expressing different selection methods for abductive explanations. Core metatheoretic properties of non-monotonic consequence relations are explored within this setting and shown to provide a well-behaved foundation for abductive reasoning.