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

• URL: http://arxiv.org/abs/2511.01753v1
• Date: Mon, 03 Nov 2025 17:03:29 GMT
• Title: SM-based Semantics for Answer Set Programs Containing Conditional Literals and Arithmetic
• Authors: Zachary Hansen, Yuliya Lierler,
• Abstract summary: Conditional literals behave as nested implications within bodies of logic rules.<n>We propose a semantics for logic programs with conditional literals and arithmetic based on the SM operator.
• Score: 3.9335611819745355
• License: http://creativecommons.org/licenses/by/4.0/
• 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 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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