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

2026-01-07

Electronic Proceedings in Theoretical Computer Science

AI Summary

This study addresses the challenge of effectively modeling abductive reasoning grounded in “only-knowing” epistemic states within formal logic, while supporting nonmonotonic selection among competing explanations. To this end, the work extends Levesque’s “only-knowing” logic by introducing an abductive modal operator that integrates epistemic states with preference semantics, thereby establishing a unified abductive framework capable of nonmonotonic inference. This is the first approach to formally combine “only-knowing” epistemic conditions with abductive reasoning, proposing a modal-logic-based method for nonmonotonic abduction and rigorously formalizing multiple explanation selection mechanisms. The resulting system exhibits strong metatheoretic properties, offering a novel logical foundation for knowledge representation and reasoning.

Technology Category

• Knowledge Representation and Reasoning: Nonmonotonic Reasoning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

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.

Problem

• abduction
• only-knowing
• non-monotonic reasoning
• epistemic logic
• modal logic

Innovation

• only-knowing
• abduction
• non-monotonic reasoning
• modal logic
• epistemic states