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Revisiting Explicit Negation in Answer Set Programming

Published online by Cambridge University Press:  20 September 2019

FELICIDAD AGUADO
Affiliation:
Information Retrieval Lab, Centro de Investigación en Tecnoloxías da Información e as Comunicacións (CITIC), Universidade da Coruña, Spain (e-mails: aguado@udc.es, cabalar@udc.es)
PEDRO CABALAR
Affiliation:
Information Retrieval Lab, Centro de Investigación en Tecnoloxías da Información e as Comunicacións (CITIC), Universidade da Coruña, Spain (e-mails: aguado@udc.es, cabalar@udc.es)
JORGE FANDINNO
Affiliation:
IRIT, University of Toulouse, CNRS, France (e-mail: jorge.fandinno@irit.fr) Universität Potsdam, Germany (e-mail: fandinno@uni-potsdam.de)
DAVID PEARCE
Affiliation:
Universidad Politécnica de Madrid, Spain (e-mail: david.pearce@upm.es)
GILBERTO PÉREZ
Affiliation:
Information Retrieval Lab, Centro de Investigación en Tecnoloxías da Información e as Comunicacións (CITIC), Universidade da Coruña, Spain (e-mails: gperez@udc.es, eicovima@udc.es)
CONCEPCIÓN VIDAL
Affiliation:
Information Retrieval Lab, Centro de Investigación en Tecnoloxías da Información e as Comunicacións (CITIC), Universidade da Coruña, Spain (e-mails: gperez@udc.es, eicovima@udc.es)
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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.

Type
Original Article
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© Cambridge University Press 2019

Footnotes

*

This work was partially supported by MINECO, Spain, grant TIC2017-84453-P, Xunta de Galicia, Spain (GPC ED431B 2019/03 and 2016-2019 ED431G/01, CITIC). The third author is funded by the Centre International de Mathématiques et d’Informatique de Toulouse (CIMI) through contract ANR-11-LABEX-0040-CIMI within the programme ANR-11-IDEX-0002-02 and the Alexander von Humboldt Foundation.

References

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