Revisiting Explicit Negation in Answer Set Programming

A common feature in Answer Set Programming is the use of a seco nd negation, stronger than default negation and sometimes called explicit, strong or classica l negation. This explicit negation is normally used in front of atoms, rather than allowing its use as a regular op erator. 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 pr ove that it can be captured by an extension of Equilibrium Logic with this second negation. We study som e properties of this variant and compare to the already known combination of Equilibrium Logic with Nel son's strong negation.