# Applying Answer Set Programming with Fuzzy Membership Functions: a Case Study

arXiv: https://arxiv.org/abs/2607.03550 · HTML: https://mlsanity.com/paper/2607.03550/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 28 references that are in the map.
- First posted on arXiv 3 Jul 2026.

## Builds on (most cited first, 5 of 5)

- [Logic Tensor Networks](https://mlsanity.com/paper/2012.13635/) (2020)
- [NeurASP: Embracing Neural Networks into Answer Set Programming](https://mlsanity.com/paper/2307.07700/) (2023)
- [Fuzzy Datalog^exists over Arbitrary t-Norms](https://mlsanity.com/paper/2403.02933/) (2024)
- [Syntax and semantics of multi-adjoint normal logic programming](https://mlsanity.com/paper/2409.14901/) (2024)
- [Extended multi-adjoint logic programming](https://mlsanity.com/paper/2410.04794/) (2024)

## Abstract (arXiv)

Human reasoning often operates through qualitative concepts expressed by linguistic labels such as high, low, expensive, or cheap, whose interpretation depends on context and is usually vague, despite being rooted in numerical data. This paper explores a novel fuzzy-logic-based qualitative extension of Answer Set Programming (ASP) to bridge numerical information and qualitative reasoning. The underlying language, formally introduced in a separate work, provides a principled framework that avoids rigid thresholds and supports robust reasoning under vagueness. Focusing on a representative use case, we illustrate how the framework integrates numerically grounded inputs (such as outputs of machine learning models) with symbolic reasoning over qualitative labels. Key features, including learning-based membership functions and semantically enriched predicates, enable the combination of expert knowledge, contextual factors, and subjective interpretations within a unified declarative setting.