@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}
}
@misc{Fandinno2019,
  author    = {Fandinno, Jorge},
  title     = {Founded (auto)epistemic equilibrium logic satisfies epistemic splitting},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {1060},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-46968},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-469685},
  pages     = {671 -- 687},
  year      = {2019},
  abstract  = {In a recent line of research, two familiar concepts from logic programming semantics (unfounded sets and splitting) were extrapolated to the case of epistemic logic programs. The property of epistemic splitting provides a natural and modular way to understand programs without epistemic cycles but, surprisingly, was only fulfilled by Gelfond's original semantics (G91), among the many proposals in the literature. On the other hand, G91 may suffer from a kind of self-supported, unfounded derivations when epistemic cycles come into play. Recently, the absence of these derivations was also formalised as a property of epistemic semantics called foundedness. Moreover, a first semantics proved to satisfy foundedness was also proposed, the so-called Founded Autoepistemic Equilibrium Logic (FAEEL). In this paper, we prove that FAEEL also satisfies the epistemic splitting property something that, together with foundedness, was not fulfilled by any other approach up to date. To prove this result, we provide an alternative characterisation of FAEEL as a combination of G91 with a simpler logic we called Founded Epistemic Equilibrium Logic (FEEL), which is somehow an extrapolation of the stable model semantics to the modal logic S5.},
  language  = {en}
}