# A Unifying Framework for Semiring-Based Constraint Logic Programming With Negation (full version)

arXiv: https://arxiv.org/abs/2507.16067 · HTML: https://mlsanity.com/paper/2507.16067/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 39 references that are in the map.
- First posted on arXiv 21 Jul 2025.

## Builds on (most cited first, 7 of 7)

- [A Uniform Treatment of Aggregates and Constraints in Hybrid ASP](https://mlsanity.com/paper/2003.04176/) (2020)
- [An ASP semantics for Constraints involving Conditional Aggregates](https://mlsanity.com/paper/2002.06911/) (2020)
- [Semirings for Probabilistic and Neuro-Symbolic Logic Programming](https://mlsanity.com/paper/2402.13782/) (2024)
- [Convergence of Datalog over (Pre-) Semirings](https://mlsanity.com/paper/2105.14435/) (2021)
- [Non-Deterministic Approximation Fixpoint Theory and Its Application in Disjunctive Logic Programming](https://mlsanity.com/paper/2211.17262/) (2022)
- [Conditional independence on semiring relations](https://mlsanity.com/paper/2310.01910/) (2023)
- [An Algebraic Notion of Conditional Independence, and Its Application to Knowledge Representation (full version)](https://mlsanity.com/paper/2412.13712/) (2024)

## Abstract (arXiv)

Constraint Logic Programming (CLP) is a logic programming formalism used to solve problems requiring the consideration of constraints, like resource allocation and automated planning and scheduling. It has previously been extended in various directions, for example to support fuzzy constraint satisfaction, uncertainty, or negation, with different notions of semiring being used as a unifying abstraction for these generalizations. None of these extensions have studied clauses with negation allowed in the body. We investigate an extension of CLP which unifies many of these extensions and allows negation in the body. We provide semantics for such programs, using the framework of approximation fixpoint theory, and give a detailed overview of the impacts of properties of the semirings on the resulting semantics. As such, we provide a unifying framework that captures existing approaches and allows extending them with a more expressive language.