# Fuzzy Lattice-based Description Logic

arXiv: https://arxiv.org/abs/2506.05833 · HTML: https://mlsanity.com/paper/2506.05833/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 19 references that are in the map.
- First posted on arXiv 6 Jun 2025.

## Builds on (most cited first, 2 of 2)

- [Rough concepts](https://mlsanity.com/paper/1907.00359/) (2019)
- [Unified Correspondence as a Proof-Theoretic Tool](https://mlsanity.com/paper/1603.08204/) (2016)

## Abstract (arXiv)

Recently, description logic LE-ALC was introduced for reasoning in the semantic environment of enriched formal contexts, and a polynomial-time tableaux algorithm was developed to check the consistency of knowledge bases with acyclic TBoxes. In this work, we introduce a fuzzy generalization of LE-ALC called LE-FALC which provides a description logic counterpart of many-valued normal non-distributive logic a.k.a. many-valued LE-logic. This description logic can be used to represent and reason about knowledge in the formal framework of fuzzy formal contexts and fuzzy formal concepts. We provide a tableaux algorithm that provides a complete and sound polynomial-time decision procedure to check the consistency of LE-FALC ABoxes. As a result, we also obtain an exponential-time decision procedure for checking the consistency of LE-FALC with acyclic TBoxes by unraveling.