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Semantics for Conditional Literals via the SM Operator

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Logic Programming and Nonmonotonic Reasoning (LPNMR 2022)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13416))

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Abstract

Conditional literals are an expressive Answer Set Programming language construct supported by the solver clingo. Their semantics are currently defined by a translation to infinitary propositional logic, however, we develop an alternative characterization with the SM operator which does not rely on grounding. This allows us to reason about the behavior of a broad class of clingo programs/encodings containing conditional literals, without referring to a particular input/instance of an encoding. We formalize the intuition that conditional literals behave as nested implications, and prove the equivalence of our semantics to those implemented by clingo.

Z. Hansen and Y. Lierler—These authors contributed equally.

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Acknowledgements

The work was partially supported by NSF grant 1707371. We are grateful to Jorge Fandinno, Vladimir Lifschitz, and Miroslaw Truszczynski for valuable discussions and comments on this paper.

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Authors and Affiliations

  1. University of Nebraska Omaha, Omaha, NE, 68182, USA

    Zachary Hansen & Yuliya Lierler

Authors
  1. Zachary Hansen
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  2. Yuliya Lierler
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Correspondence to Yuliya Lierler .

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Editors and Affiliations

  1. University of Oxford, Oxford, UK

    Georg Gottlob

  2. Miami University, Oxford, OH, USA

    Daniela Inclezan

  3. University of Genova, Genoa, Italy

    Marco Maratea

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Hansen, Z., Lierler, Y. (2022). Semantics for Conditional Literals via the SM Operator. In: Gottlob, G., Inclezan, D., Maratea, M. (eds) Logic Programming and Nonmonotonic Reasoning. LPNMR 2022. Lecture Notes in Computer Science(), vol 13416. Springer, Cham. https://doi.org/10.1007/978-3-031-15707-3_20

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  • DOI: https://doi.org/10.1007/978-3-031-15707-3_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-15706-6

  • Online ISBN: 978-3-031-15707-3

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