FLINGO -- Instilling ASP Expressiveness into Linear Integer Constraints

2026-02-10

AI Summary

This work addresses the limited expressiveness of current Constraint Answer Set Programming (CASP) solvers when handling numerical constraints, which often forfeits key features of Answer Set Programming (ASP), such as default reasoning, undefined attributes, non-deterministic choices, and aggregates. To bridge this gap, the paper introduces FLINGO, a novel language that, for the first time, integrates ASP-style declarative modeling of numerical attributes into linear integer constraints. FLINGO achieves this by employing a syntactic translation mechanism that compiles its constructs into standard CLINGCON input. The approach preserves the efficiency of state-of-the-art numerical constraint solving while substantially enhancing modeling expressiveness. A prototype implementation demonstrates the effectiveness and practicality of the proposed method across several illustrative examples.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Logic Programming
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Multilingual and cross-lingual Web search

Abstract

Constraint Answer Set Programming (CASP) is a hybrid paradigm that enriches Answer Set Programming (ASP) with numerical constraint processing, something required in many real-world applications. The usual specification of constraints in most CASP solvers is closer to the numerical back-end expressiveness and semantics, rather than to standard specification in ASP. In the latter, numerical attributes are represented with predicates and this allows declaring default values, leaving the attribute undefined, making non-deterministic assignments with choice rules or using aggregated values. In CASP, most (if not all) of these features are lost once we switch to a constraint-based representation of those same attributes. In this paper, we present the FLINGO language (and tool) that incorporates the aforementioned expressiveness inside the numerical constraints and we illustrate its use with several examples. Based on previous work that established its semantic foundations, we also present a translation from the newly introduced FLINGO syntax to regular CASP programs following the CLINGCON input format.

Problem

• Constraint Answer Set Programming
• Answer Set Programming
• numerical constraints
• expressiveness
• FLINGO

Innovation

• Constraint Answer Set Programming
• FLINGO
• numerical constraints
• ASP expressiveness
• CLINGCON