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

2025/11/03 by Hansen, Zachary, Lierler, Yuliya
Computer Science · #Artificial Intelligence (cs.AI) #F.4.1 #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Multi-Agent Systems and Negotiation #Programming Languages (cs.PL) #Semantic Web and Ontologies

paper · doi:10.48550/arxiv.2511.01753

openalex publication_date 2025/11/03 · openalex created_date 2025/11/06 · openalex updated_date 2026/07/28

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.

Citations

• External Behavior of a Logic Program and Verification of Refactoring
• Verification of Locally Tight Programs
• Experimenting with robotic intra-logistics domains

Related

• A framework for Conditional Reasoning in Answer Set Programming
• Justifications for Logic Programs under Answer Set Semantics
• Historical Review of Variants of Informal Semantics for Logic Programs under Answer Set Semantics: GL'88, GL'91, GK'14, D-V'12
• The informal semantics of Answer Set Programming: A Tarskian perspective
• Answer Set Programming Made Easy