Propositional Abduction via Only-Knowing: A Non-Monotonic Approach
Sanderson Molick, Vaishak Belle
TL;DR
The paper addresses how to formalize abductive reasoning when an agent's knowledge is constrained by Levesque's logic of only-knowing. It introduces the Logic of Only-Knowing and Abduction (AOL) by defining an abductive modality A through the interaction of only-knowing O and knowing K, enabling abductive inferences within explicit background knowledge. It then extends AOL with a plausibility-driven non-monotonic layer AOL_prec, establishing minimal-explanation concepts and multiple selection criteria (subset-minimal, cardinality-minimal, priorization) and proving key metatheoretical properties, including minimal-model existence and conditions under which selection methods align with preferential entailment. The work provides a principled, knowledge-bounded foundation for abductive reasoning with tunable non-monotonic selection mechanisms, with potential extensions to proof theory and multi-agent settings.
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.