# Complexity of Faceted Explanations in Propositional Abduction

arXiv: https://arxiv.org/abs/2507.14962 · HTML: https://mlsanity.com/paper/2507.14962/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 10 of its 50 references that are in the map.
- First posted on arXiv 20 Jul 2025.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 10 of 10)

- [Explanation in Artificial Intelligence: Insights from the Social Sciences](https://mlsanity.com/paper/1706.07269/) (2017)
- [Abduction-Based Explanations for Machine Learning Models](https://mlsanity.com/paper/1811.10656/) (2018)
- [Eliminating The Impossible, Whatever Remains Must Be True](https://mlsanity.com/paper/2206.09551/) (2022)
- [Rushing and Strolling among Answer Sets -- Navigation Made Easy](https://mlsanity.com/paper/2112.07596/) (2021)
- [Efficient Rectification of Neuro-Symbolic Reasoning Inconsistencies by Abductive Reflection](https://mlsanity.com/paper/2412.08457/) (2024)
- [Facets in Argumentation: A Formal Approach to Argument Significance](https://mlsanity.com/paper/2505.10982/) (2025)
- [Backdoors to Abduction](https://mlsanity.com/paper/1304.5961/) (2013)
- [Counting and Reasoning with Plans](https://mlsanity.com/paper/2502.00145/) (2025)
- [Strong Backdoors for Default Logic](https://mlsanity.com/paper/1602.06052/) (2016)
- [Epistemic Logic Programs: Non-Ground and Counting Complexity](https://mlsanity.com/paper/2503.04731/) (2025)

## Built on by (most cited first, 1 of 1)

- [Representative Sets in Propositional Abduction](https://mlsanity.com/paper/2607.21183/) (2026)

## Abstract (arXiv)

Abductive reasoning is a popular non-monotonic paradigm that aims to explain observed symptoms and manifestations. It has many applications, such as diagnosis and planning in artificial intelligence and database updates. In propositional abduction, we focus on specifying knowledge by a propositional formula. The computational complexity of tasks in propositional abduction has been systematically characterized - even with detailed classifications for Boolean fragments. Unsurprisingly, the most insightful reasoning problems (counting and enumeration) are computationally highly challenging. Therefore, we consider reasoning between decisions and counting, allowing us to understand explanations better while maintaining favorable complexity. We introduce facets to propositional abductions, which are literals that occur in some explanation (relevant) but not all explanations (dispensable). Reasoning with facets provides a more fine-grained understanding of variability in explanations (heterogeneous). In addition, we consider the distance between two explanations, enabling a better understanding of heterogeneity/homogeneity. We comprehensively analyze facets of propositional abduction in various settings, including an almost complete characterization in Post's framework.