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

TL;DR

This paper introduces a new semantics for answer set programs with conditional literals and arithmetic, based on the SM operator, avoiding grounding and aligning with existing semantics.

Contribution

It proposes a semantics for logic programs with conditional literals and arithmetic using the SM operator, eliminating the need for grounding.

Findings

Semantics based on the SM operator for programs with conditional literals.

Establishes correspondence with existing semantics.

Avoids grounding in the semantics of such programs.

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.