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

arXiv: https://arxiv.org/abs/2511.01753 · HTML: https://mlsanity.com/paper/2511.01753/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 35 references that are in the map.
- First posted on arXiv 3 Nov 2025.

## Builds on (most cited first, 6 of 6)

- [Verifying Tight Logic Programs with anthem and Vampire](https://mlsanity.com/paper/2008.02025/) (2020)
- [Experimenting with robotic intra-logistics domains](https://mlsanity.com/paper/1804.10247/) (2018)
- [Train Scheduling with Hybrid Answer Set Programming](https://mlsanity.com/paper/2003.08598/) (2020)
- [Modular Answer Set Programming as a Formal Specification Language](https://mlsanity.com/paper/2008.02015/) (2020)
- [Verification of Locally Tight Programs](https://mlsanity.com/paper/2204.10789/) (2022)
- [External Behavior of a Logic Program and Verification of Refactoring](https://mlsanity.com/paper/2305.17485/) (2023)

## Built on by (most cited first, 1 of 1)

- [Parametric Modular Answer Set Programs Made Declarative](https://mlsanity.com/paper/2605.22716/) (2026)

## Abstract (arXiv)

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.