# Probabilistic Models of Relational Implication

arXiv: https://arxiv.org/abs/1907.12048 · HTML: https://mlsanity.com/paper/1907.12048/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jul 2019.

## Built on by (most cited first, 17 of 17)

- [Sources of Hallucination by Large Language Models on Inference Tasks](https://mlsanity.com/paper/2305.14552/) (2023)
- [AbsPyramid: Benchmarking the Abstraction Ability of Language Models with a Unified Entailment Graph](https://mlsanity.com/paper/2311.09174/) (2023)
- [AbsInstruct: Eliciting Abstraction Ability from LLMs through Explanation Tuning with Plausibility Estimation](https://mlsanity.com/paper/2402.10646/) (2024)
- [TaxoLLaMA: WordNet-based Model for Solving Multiple Lexical Semantic Tasks](https://mlsanity.com/paper/2403.09207/) (2024)
- [Entailment Graph Learning with Textual Entailment and Soft Transitivity](https://mlsanity.com/paper/2204.03286/) (2022)
- [Multivalent Entailment Graphs for Question Answering](https://mlsanity.com/paper/2104.07846/) (2021)
- [Language Models for Lexical Inference in Context](https://mlsanity.com/paper/2102.05331/) (2021)
- [Smoothing Entailment Graphs with Language Models](https://mlsanity.com/paper/2208.00318/) (2022)
- [Cross-lingual Inference with A Chinese Entailment Graph](https://mlsanity.com/paper/2203.06264/) (2022)
- [Language Models Are Poor Learners of Directional Inference](https://mlsanity.com/paper/2210.04695/) (2022)
- [Continuous Entailment Patterns for Lexical Inference in Context](https://mlsanity.com/paper/2109.03695/) (2021)
- [Neutralizing Bias in LLM Reasoning using Entailment Graphs](https://mlsanity.com/paper/2503.11614/) (2025)
- [Blindness to Modality Helps Entailment Graph Mining](https://mlsanity.com/paper/2109.10227/) (2021)
- [From the One, Judge of the Whole: Typed Entailment Graph Construction with Predicate Generation](https://mlsanity.com/paper/2306.04170/) (2023)
- [Explicit Inductive Inference using Large Language Models](https://mlsanity.com/paper/2408.14467/) (2024)
- [S2LPP: Small-to-Large Prompt Prediction across LLMs](https://mlsanity.com/paper/2505.20097/) (2025)
- [LLMs are Frequency Pattern Learners in Natural Language Inference](https://mlsanity.com/paper/2505.21011/) (2025)

## Abstract (arXiv)

Relational data in its most basic form is a static collection of known facts. However, by learning to infer and deduct additional information and structure, we can massively increase the usefulness of the underlying data. One common form of inferential reasoning in knowledge bases is implication discovery. Here, by learning when one relation implies another, we can extend our knowledge representation. There are several existing models for relational implication, however we argue they are motivated but not principled. To this end, we define a formal probabilistic model of relational implication. By using estimators based on the empirical distribution of our dataset, we demonstrate that our model outperforms existing approaches. While previous work achieves a best score of 0.7812 AUC on an evaluatory dataset, our ProbE model improves this to 0.7915. Furthermore, we demonstrate that our model can be improved substantially through the use of link prediction models and dense latent representations of the underlying argument and relations. This variant, denoted ProbL, improves the state of the art on our evaluation dataset to 0.8143. In addition to developing a new framework and providing novel scores of relational implication, we provide two pragmatic resources to assist future research. First, we motivate and develop an improved crowd framework for constructing labelled datasets of relational implication. Using this, we reannotate and make public a dataset comprised of 17,848 instances of labelled relational implication. We demonstrate that precision (as evaluated by expert consensus with the crowd labels) on the resulting dataset improves from 53% to 95%.