---
title: "Non-expansive Fuzzy ALC"
authors:
  - "Stefan Gebhart"
  - "Lutz Schröder"
  - "Paul Wild"
doi: "10.24963/ijcai.2025/502"
url: "https://ijcai.org/proceedings/2025/502"
pdf: "https://ijcai.org/proceedings/2025/0502.pdf"
venue: "Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence"
year: 2025
pages: "4509-4517"
track: "Main Track"
keywords:
  - "Knowledge Representation and Reasoning: KRR: Computational complexity of reasoning"
  - "Knowledge Representation and Reasoning: KRR: Description logics and ontologies"
  - "Knowledge Representation and Reasoning: KRR: Knowledge representation languages"
---

# Non-expansive Fuzzy ALC

Stefan Gebhart, Lutz Schröder, Paul Wild

*Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence*, pages 4509-4517. DOI: [10.24963/ijcai.2025/502](https://doi.org/10.24963/ijcai.2025/502)

## Abstract

Fuzzy description logics serve the representation of vague knowledge, typically letting concepts take truth degrees in the unit interval. Expressiveness, logical properties, and complexity vary strongly with the choice of propositional base. The Łukasiewicz propositional base is generally perceived to have preferable logical properties but often entails high complexity or even undecidability. Contrastingly, the less expressive Zadeh propositional base comes with low complexity but entails essentially no change in logical behaviour compared to the classical case. To strike a balance between these poles, we propose non-expansive fuzzy ALC, in which the Zadeh base is extended with Łukasiewicz connectives where one side is restricted to be a rational constant, that is, with constant shift operators. This allows, for instance, modelling dampened inheritance of properties along roles. We present an unlabelled tableau method for non-expansive fuzzy ALC, which allows reasoning over general TBoxes in EXPTime like in two-valued ALC.