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

arXiv: https://arxiv.org/abs/2601.04272 · HTML: https://mlsanity.com/paper/2601.04272/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 23 references that are in the map.
- First posted on arXiv 7 Jan 2026.

## Builds on (most cited first, 1 of 1)

- [Neural-Symbolic Integration: A Compositional Perspective](https://mlsanity.com/paper/2010.11926/) (2020)

## Abstract (arXiv)

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.