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SM-Based Semantics for Answer Set Programs Containing Conditional Literals and Arithmetic

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Practical Aspects of Declarative Languages (PADL 2025)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 15537))

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Abstract

Modern answer set programming solvers such as clingo support advanced language constructs that improve the expressivity and conciseness of logic programs. Conditional literals are one such construct. They form “subformulas” that behave as nested implications within the bodies of logic rules. Their inclusion brings the form of rules closer to the less restrictive syntax of first-order logic. These qualities make conditional literals useful tools for knowledge representation. In this paper, we propose a semantics for logic programs with conditional literals and arithmetic based on the \(\text {SM}\) operator. These semantics do not require grounding, unlike the established semantics for such programs that relies on a translation to infinitary propositional logic. The main result of this paper establishes the precise correspondence between the proposed and existing semantics.

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Notes

  1. 1.

    https://github.com/potassco/anthem.

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Acknowledgments

We are grateful to Jorge Fandinno and Vladimir Lifschitz for their valuable comments, and to our anonymous reviewers for their feedback.

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Authors and Affiliations

  1. University of Nebraska Omaha, Omaha, NE, 68106, USA

    Zachary Hansen & Yuliya Lierler

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

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Editors and Affiliations

  1. Sabanci University, Istanbul, Türkiye

    Esra Erdem

  2. Universitat Politècnica de València, Valencia, Valencia, Spain

    Germán Vidal

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Hansen, Z., Lierler, Y. (2025). SM-Based Semantics for Answer Set Programs Containing Conditional Literals and Arithmetic. In: Erdem, E., Vidal, G. (eds) Practical Aspects of Declarative Languages. PADL 2025. Lecture Notes in Computer Science, vol 15537. Springer, Cham. https://doi.org/10.1007/978-3-031-84924-4_5

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  • DOI: https://doi.org/10.1007/978-3-031-84924-4_5

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