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

2025-07-21

AI Summary

Constraint Logic Programming (CLP) lacks native support for negation in rule bodies, and existing extensions—such as fuzzy, probabilistic, or uncertain constraints—lack a unified semantic foundation. Method: This work proposes a unified, negation-enhanced CLP model based on the semantic ring framework. It introduces, for the first time in semantic-ring CLP, a formal mechanism for negation within rule bodies; constructs program semantics for negated clauses using approximate fixed-point theory; and formally characterizes how algebraic properties of the semantic ring—e.g., commutativity and zero-absorption—affect model semantics. Contribution/Results: The framework uniformly accommodates diverse constraint extensions—including fuzzy, probabilistic, and uncertain constraints—thereby significantly enhancing CLP’s expressive power and semantic composability. It provides both a rigorous theoretical foundation and a practical implementation pathway for unified modeling of heterogeneous, multi-source constraints.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Logic Programming
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• Extends CLP to unify semiring-based extensions with negation
• Provides semantics for programs using approximation fixpoint theory
• Analyzes semiring properties' impact on resulting semantics

Innovation

• Extends CLP with negation in body
• Uses semiring framework for unification
• Applies approximation fixpoint theory semantics