# Default Logic and Bounded Treewidth

arXiv: https://arxiv.org/abs/1706.09393 · HTML: https://mlsanity.com/paper/1706.09393/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jun 2017.

## Built on by (most cited first, 2 of 2)

- [Facets in Argumentation: A Formal Approach to Argument Significance](https://mlsanity.com/paper/2505.10982/) (2025)
- [Epistemic Logic Programs: Non-Ground and Counting Complexity](https://mlsanity.com/paper/2503.04731/) (2025)

## Abstract (arXiv)

In this paper, we study Reiter's propositional default logic when the treewidth of a certain graph representation (semi-primal graph) of the input theory is bounded. We establish a dynamic programming algorithm on tree decompositions that decides whether a theory has a consistent stable extension (Ext). Our algorithm can even be used to enumerate all generating defaults (ExtEnum) that lead to stable extensions. We show that our algorithm decides Ext in linear time in the input theory and triple exponential time in the treewidth (so-called fixed-parameter linear algorithm). Further, our algorithm solves ExtEnum with a pre-computation step that is linear in the input theory and triple exponential in the treewidth followed by a linear delay to output solutions.