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Deontic Equilibrium Logic with eXplicit Negation

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Logics in Artificial Intelligence (JELIA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14281))

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Abstract

Equilibrium logic is a logical characterization of Answer Set Programming (ASP). We introduce Deontic Equilibrium Logic with eXplicit negation (DELX), its extension for normative reasoning. In contrast to modal approaches, DELX utilizes a normal form that restricts deontic operators solely to atoms. We establish that any theories in DELX can be reduced to ASP, and demonstrate the efficacy of this minimalist approach in addressing key challenges from the defeasible deontic logic literature.

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Notes

  1. 1.

    In the ASP-core-2 input language, \(\leftarrow , \lnot \) and \(\wedge \) are represented as ‘:-’, ‘-’ and commas.

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Acknowledgments

Work partially supported by the WWTF project ICT22-023, by the Spanish Ministry of Science and Innovation, Spain, MCIN/AEI/10.13039/501100011033 (grant PID2020-116201GB-I00), by Xunta de Galicia, Spain and the European Union (grant GPC ED431B 2022/33) and by project LIANDA - BBVA Foundation Grants for Scientific Research Projects, Spain.

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Authors and Affiliations

  1. University of A Coruña, A Coruña, Spain

    Pedro Cabalar

  2. TU Wien, Vienna, Austria

    Agata Ciabattoni

  3. University of Luxembourg, Luxembourg City, Luxembourg

    Leendert van der Torre

Authors
  1. Pedro Cabalar
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  2. Agata Ciabattoni
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  3. Leendert van der Torre
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Correspondence to Pedro Cabalar .

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Editors and Affiliations

  1. TU Dresden, Dresden, Germany

    Sarah Gaggl

  2. Artificial Intelligence Research Institute - IIIA CSIC, Barcelona, Spain

    Maria Vanina Martinez

  3. Umeå University, Umeå, Sweden

    Magdalena Ortiz

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Cabalar, P., Ciabattoni, A., van der Torre, L. (2023). Deontic Equilibrium Logic with eXplicit Negation. In: Gaggl, S., Martinez, M.V., Ortiz, M. (eds) Logics in Artificial Intelligence. JELIA 2023. Lecture Notes in Computer Science(), vol 14281. Springer, Cham. https://doi.org/10.1007/978-3-031-43619-2_34

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