Faithful Rule Learning for Tabular Cell Completion

Tabular cell completion aims to infer values that can fill missing cells in incomplete table rows. While machine learning models have achieved strong performance on this task, their limited interpretability restricts their applicability in high-stakes domains. In this paper, we introduce two interpretable models for tabular cell completion based on path-based relational patterns. Given an incomplete row and a candidate value, the models aggregate evidence from paths connecting the known constants in the row to the candidate value. A key feature of our approach is that the learned models admit *faithful* symbolic characterizations in the form of equivalent Datalog programs: for every model instance, we show how to extract an equivalent Datalog program that produces exactly the same outputs on every database over the underlying schema. We further analyze the relationship between the two models, showing how different aggregation mechanisms lead to distinct trade-offs between expressive power and simplicity of rule extraction. Experimental results demonstrate strong performance on tabular cell completion benchmarks while additionally providing human-readable explanations with formal faithfulness guarantees.