Bound-Founded Semantics for Answer Set Programming with Difference Constraints: Preliminary Report

2026-07-23 · Source: Artificial Intelligence · Field: Technology & Digital — Artificial Intelligence & Machine Learning · Depth: Expert, quick

Summary

A new many-sorted variant of the Bound-founded Logic of Here-and-There (HTb) is introduced to establish a unified logical foundation for Answer Set Programming (ASP) integrated with linear constraints. This framework addresses the current reliance of hybrid solvers on disparate semantic underpinnings. The research applies HTb to the domain of difference constraints, specifically focusing on the semantic characterization of clingo[DL]. A central aspect of this approach is the formalization of foundedness for numeric variables. By investigating how hybrid systems such as clingo[DL], clingcon, and flingo justify constraint atoms, the framework reveals the semantic origins of their differing behaviors. This work yields a single, consistent framework that formalizes existing systems like clingo[DL] and supports the rigorous study of program simplifications and the future integration of diverse semantic principles.

Key takeaway

For AI Scientists and logic programmers developing or extending Answer Set Programming (ASP) systems with linear constraints, this work provides a critical unified semantic framework. You should recognize that disparate semantic underpinnings in current hybrid solvers can lead to unpredictable behavior. Adopting the Bound-founded Logic of Here-and-There (HTb) offers a consistent foundation to rigorously characterize system semantics, study program simplifications, and integrate new principles, ensuring more robust and predictable system designs.

Key insights

Unified logical foundation for ASP with linear constraints via Bound-founded Logic of Here-and-There (HTb).

Principles

• Hybrid ASP solvers often lack unified logical foundations.
• Foundedness for numeric variables is key to semantic characterization.
• Different constraint atom justifications lead to varying system behaviors.

Method

Introduce many-sorted HTb, formalize foundedness for numeric variables, then apply to difference constraints to characterize hybrid systems like clingo[DL].

In practice

• Characterize clingo[DL]'s semantics.
• Study program simplifications rigorously.
• Integrate diverse semantic principles.

Topics

• Answer Set Programming
• Logic Programming
• Constraint Programming
• Bound-founded Logic of Here-and-There
• clingo[DL]
• Semantic Foundations
• Difference Constraints

Best for: Research Scientist, AI Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Artificial Intelligence.