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

• URL: http://arxiv.org/abs/2601.04272v1
• Date: Wed, 07 Jan 2026 12:03:26 GMT
• Title: Propositional Abduction via Only-Knowing: A Non-Monotonic Approach
• Abstract summary: The paper introduces a basic logic of knowledge and abduction by extending Levesque logic of only-knowing.<n>The upshot is an alternative approach to abduction that employs a modal vocabulary.
• Score: 2.1168653123022634
• License: http://creativecommons.org/licenses/by/4.0/
• 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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