# On Uniform Equivalence of Epistemic Logic Programs

## TL;DR

This paper characterizes uniform equivalence in Epistemic Logic Programs, extending concepts from ASP, and analyzes the computational complexity of deciding such equivalence, which is on the third level of the polynomial hierarchy.

## Contribution

It provides the first characterization of uniform equivalence for ELPs and studies the complexity of deciding this equivalence.

## Key findings

- Uniform equivalence characterization for ELPs applicable to modern solvers
- Deciding uniform equivalence for ELPs is on the third level of the polynomial hierarchy
- Complexity results inform the design of modular ELP systems

## Abstract

Epistemic Logic Programs (ELPs) extend Answer Set Programming (ASP) with epistemic negation and have received renewed interest in recent years. This led to the development of new research and efficient solving systems for ELPs. In practice, ELPs are often written in a modular way, where each module interacts with other modules by accepting sets of facts as input, and passing on sets of facts as output. An interesting question then presents itself: under which conditions can such a module be replaced by another one without changing the outcome, for any set of input facts? This problem is known as uniform equivalence, and has been studied extensively for ASP. For ELPs, however, such an investigation is, as of yet, missing. In this paper, we therefore propose a characterization of uniform equivalence that can be directly applied to the language of state-of-the-art ELP solvers. We also investigate the computational complexity of deciding uniform equivalence for two ELPs, and show that it is on the third level of the polynomial hierarchy.