Revisiting Explicit Negation in Answer Set Programming
This work addresses a theoretical limitation in Answer Set Programming for researchers in logic programming and knowledge representation, but appears incremental as it builds on existing frameworks.
The paper tackles the problem of arbitrary combination of explicit negation with nested expressions in Answer Set Programming by extending the reduct concept and proving it can be captured by an extension of Equilibrium Logic with this second negation. The result includes a study of properties and comparison to known combinations with Nelson's strong negation.
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.