Verifiable Knowledge Expansion through Retrieval-Grounded Formal Concept Analysis

2026-07-02

AI Summary

This study addresses the lack of verifiability and consistency in knowledge generated by language models by proposing a novel approach that integrates Formal Concept Analysis (FCA) with a retrieval-augmented small language model (SLM). For the first time, FCA is embedded into the SLM knowledge construction pipeline as a symbolic verification mechanism, enabling traceable and auditable knowledge expansion through entailment validation, counterexample generation, consistency checking, and attribute suggestion. Experiments on a rare ataxia dataset yield relation F1 scores ranging from 0.29 to 0.52 and entailment F1 scores from 0.22 to 0.30 across ten random seeds. Expanding the seed set substantially increases both the quantity and performance of entailment evaluations, while ablation studies confirm that retrieval-based instance judgment critically contributes to entailment scoring.

Abstract

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.

Problem

• knowledge expansion
• ontology construction
• formal concept analysis
• retrieval-augmented language models
• knowledge verification

Innovation

• retrieval-augmented SLM
• formal concept analysis
• symbolic verification
• knowledge expansion
• implication validation