Propositional Abduction via Only-Knowing: A Non-Monotonic Approach
This work addresses the problem of formalizing abductive reasoning in logic for researchers in AI and knowledge representation, but it is incremental as it builds on existing modal logic frameworks.
The paper tackles the problem of propositional abduction by extending Levesque's logic of only-knowing with a modal operator and a preferential relation, resulting in a non-monotonic framework for selecting abductive explanations. It establishes core metatheoretic properties to provide a well-behaved foundation for abductive reasoning.
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.