# Minimal Model Counting via Knowledge Compilation

arXiv: https://arxiv.org/abs/2409.10170 · HTML: https://mlsanity.com/paper/2409.10170/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Sep 2024.

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

- [An ASP-Based Framework for MUSes](https://mlsanity.com/paper/2507.03929/) (2025)
- [Counting Answer Sets of Disjunctive Answer Set Programs](https://mlsanity.com/paper/2507.11655/) (2025)

## Abstract (arXiv)

Counting the number of models of a Boolean formula is a fundamental problem in artificial intelligence and reasoning. Minimal models of a Boolean formula are critical in various reasoning systems, making the counting of minimal models essential for detailed inference tasks. Existing research primarily focused on decision problems related to minimal models. In this work, we extend beyond decision problems to address the challenge of counting minimal models. Specifically, we propose a novel knowledge compilation form that facilitates the efficient counting of minimal models. Our approach leverages the idea of justification and incorporates theories from answer set counting.