# Epistemic Logic Programs: Non-Ground and Counting Complexity

arXiv: https://arxiv.org/abs/2503.04731 · HTML: https://mlsanity.com/paper/2503.04731/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 69 references that are in the map.
- First posted on arXiv 31 Jan 2025.

## Builds on (most cited first, 12 of 12)

- [Advancing Lazy-Grounding ASP Solving Techniques -- Restarts, Phase Saving, Heuristics, and More](https://mlsanity.com/paper/2008.03526/) (2020)
- [Rushing and Strolling among Answer Sets -- Navigation Made Easy](https://mlsanity.com/paper/2112.07596/) (2021)
- [Treewidth-aware Reductions of Normal ASP to SAT -- Is Normal ASP Harder than SAT after All?](https://mlsanity.com/paper/2210.03553/) (2022)
- [selp: A Single-Shot Epistemic Logic Program Solver](https://mlsanity.com/paper/2001.01089/) (2020)
- [eclingo: A solver for Epistemic Logic Programs](https://mlsanity.com/paper/2008.02018/) (2020)
- [Constraint Solving via Fractional Edge Covers](https://mlsanity.com/paper/1711.04506/) (2017)
- [Structural Decompositions of Epistemic Logic Programs](https://mlsanity.com/paper/2001.04219/) (2020)
- [Thirty years of Epistemic Specifications](https://mlsanity.com/paper/2108.07669/) (2021)
- [Dual-normal Logic Programs - the Forgotten Class](https://mlsanity.com/paper/1507.05388/) (2015)
- [Utilizing Treewidth for Quantitative Reasoning on Epistemic Logic Programs](https://mlsanity.com/paper/2108.03022/) (2021)
- [Default Logic and Bounded Treewidth](https://mlsanity.com/paper/1706.09393/) (2017)
- [Epistemic Logic Programs: A Different World View](https://mlsanity.com/paper/1909.08233/) (2019)

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

- [Complexity of Faceted Explanations in Propositional Abduction](https://mlsanity.com/paper/2507.14962/) (2025)

## Abstract (arXiv)

Answer Set Programming (ASP) is a prominent problem-modeling and solving framework, whose solutions are called answer sets. Epistemic logic programs (ELP) extend ASP to reason about all or some answer sets. Solutions to an ELP can be seen as consequences over multiple collections of answer sets, known as world views. While the complexity of propositional programs is well studied, the non-ground case remains open. This paper establishes the complexity of non-ground ELPs. We provide a comprehensive picture for well-known program fragments, which turns out to be complete for the class NEXPTIME with access to oracles up to SigmaP2. In the quantitative setting, we establish complexity results for counting complexity beyond #EXP. To mitigate high complexity, we establish results in case of bounded predicate arity, reaching up to the fourth level of the polynomial hierarchy. Finally, we provide ETH-tight runtime results for the parameter treewidth, which has applications in quantitative reasoning, where we reason on (marginal) probabilities of epistemic literals.