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

TL;DR

This paper introduces a comprehensive framework for semiring-based Constraint Logic Programming that incorporates negation in the body, unifying various existing extensions and analyzing their semantics through approximation fixpoint theory.

Contribution

It presents a unifying semantic framework for semiring-based CLP with negation, extending previous models and analyzing the impact of semiring properties on semantics.

Findings

Provides a formal semantics for CLP with negation using approximation fixpoint theory.

Unifies multiple existing CLP extensions under a single framework.

Analyzes how semiring properties influence the semantics of the extended CLP language.

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.