@misc{AguadoCabalarFandinnoetal.2019,
  author    = {Aguado, Felicidad and Cabalar, Pedro and Fandinno, Jorge and Pearce, David and Perez, Gilberto and Vidal, Concepcion},
  title     = {Revisiting explicit negation in answer set programming},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {1104},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-46969},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-469697},
  pages     = {908 -- 924},
  year      = {2019},
  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.},
  language  = {en}
}
@inproceedings{Cabalar2010,
  author    = {Cabalar, Pedro},
  title     = {Existential quantifiers in the rule body},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-41476},
  year      = {2010},
  abstract  = {In this paper we consider a simple syntactic extension of Answer Set Programming (ASP) for dealing with (nested) existential quantifiers and double negation in the rule bodies, in a close way to the recent proposal RASPL-1. The semantics for this extension just resorts to Equilibrium Logic (or, equivalently, to the General Theory of Stable Models), which provides a logic-programming interpretation for any arbitrary theory in the syntax of Predicate Calculus. We present a translation of this syntactic class into standard logic programs with variables (either disjunctive or normal, depending on the input rule heads), as those allowed by current ASP solvers. The translation relies on the introduction of auxiliary predicates and the main result shows that it preserves strong equivalence modulo the original signature.},
  language  = {en}
}