# Verifiable Knowledge Expansion through Retrieval-Grounded Formal Concept Analysis

arXiv: https://arxiv.org/abs/2607.01773 · HTML: https://mlsanity.com/paper/2607.01773/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 16 references that are in the map.
- First posted on arXiv 2 Jul 2026.

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

- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [Retrieval Augmentation Reduces Hallucination in Conversation](https://mlsanity.com/paper/2104.07567/) (2021)
- [Unifying Large Language Models and Knowledge Graphs: A Roadmap](https://mlsanity.com/paper/2306.08302/) (2023)
- [Comparing Specialised Small and General Large Language Models on Text Classification: 100 Labelled Samples to Achieve Break-Even Performance](https://mlsanity.com/paper/2402.12819/) (2024)
- [Small Language Models in the Real World: Insights from Industrial Text Classification](https://mlsanity.com/paper/2505.16078/) (2025)

## Abstract (arXiv)

Ontology construction requires deciding which objects, attributes, and structural relations should be accepted as valid knowledge. Language models can propose such structures from text, but their outputs can still be unsupported or inconsistent. This paper proposes a retrieval-augmented small language model (SLM) framework that uses formal concept analysis (FCA) as a symbolic verification loop for knowledge expansion. Starting from seed attributes, FCA proposes implications over a growing formal context. A retrieval-grounded SLM oracle then validates each implication or returns a counterexample. The oracle also supports incidence judgments, consistency checks, and attribute proposals, making accepted implications, counterexamples, contradictions, and corrections inspectable. In a rare ataxia setting constructed from Orphadata resources, retrieval-grounded 10-seed runs obtain relation F1 of 0.29-0.52 and closure-based implication F1 of 0.22-0.30. Larger seed sets increase the number of evaluated implications and often improve implication F1. The lower implication scores reflect a stricter evaluation of derived implications, where one missed or extra relation can affect several implication judgments. Ablations show that incidence judgments in a fixed object-attribute setting can improve closure-based implication scores. However, identifying positive object-attribute pairs remains difficult even when the candidate objects and attributes are fixed.