# Revisiting Explicit Negation in Answer Set Programming

## TL;DR

This paper explores the integration of explicit negation with nested expressions in Answer Set Programming, extending existing logical frameworks and analyzing their properties and relationships.

## Contribution

It introduces an extension of Equilibrium Logic to incorporate explicit negation with nested expressions, providing a formal foundation and comparative analysis.

## Key findings

- Extended the concept of reduct for combined explicit negation and nested expressions.
- Proved that the extended syntax can be captured by an extension of Equilibrium Logic.
- Compared the new approach with existing logic systems involving strong negation.

## Abstract

A common feature in Answer Set Programming is the use of a second negation, stronger than default negation and sometimes called explicit, strong or classical negation. This explicit negation is normally used in front of atoms, rather than allowing its use as a regular operator. In this paper we consider the arbitrary combination of explicit negation with nested expressions, as those defined by Lifschitz, Tang and Turner. We extend the concept of reduct for this new syntax and then prove that it can be captured by an extension of Equilibrium Logic with this second negation. We study some properties of this variant and compare to the already known combination of Equilibrium Logic with Nelson's strong negation. Under consideration for acceptance in TPLP.