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arXiv · 2601.04272

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

Sanderson Molick·Vaishak Belle
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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.

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Sanderson Molick, Vaishak Belle. 2026-01-07. Propositional Abduction via Only-Knowing: A Non-Monotonic Approach. https://doi.org/10.4204/eptcs.439.2

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