2026/07/20 by Pedro Cabalar, Jorge Fandinno, Nicolas Rühling +3
Computer Science · #Logic, Reasoning, and Knowledge #Multi-Agent Systems and Negotiation #Semantic Web and Ontologies
paper · pdf · doi:10.4204/eptcs.450.27
While the integration of linear constraints has significantly expanded the reach of Answer Set Programming (ASP), existing hybrid solvers often rely on disparate semantic underpinnings that lack a unified logical foundation.We address this gap by introducing a many-sorted variant of the Boundfounded Logic of Here-and-There (HT b ), providing a versatile framework capable of characterizing equilibrium models across a wide spectrum of alternative semantics for extensions of ASP with linear constraints.We apply this framework to the setting of difference constraints, focusing on the semantic characterization of clingo [DL].Central to our approach is the formalization of foundedness for numeric variables.By investigating how different hybrid systems-such as clingo[DL], clingcon, and flingo-justify constraint atoms, we uncover the semantic roots of their varying behaviors.This investigation results in a single, consistent framework that not only formalizes the foundations of current systems like clingo[DL] but also facilitates the rigorous study of program simplifications and the future integration of diverse semantic principles.