# A Description Logic for Analogical Reasoning

arXiv: https://arxiv.org/abs/2105.04620 · HTML: https://mlsanity.com/paper/2105.04620/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 34 references that are in the map.
- First posted on arXiv 10 May 2021.

## Builds on (most cited first, 6 of 6)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Embedding Entities and Relations for Learning and Inference in Knowledge Bases](https://mlsanity.com/paper/1412.6575/) (2014)
- [TuckER: Tensor Factorization for Knowledge Graph Completion](https://mlsanity.com/paper/1901.09590/) (2019)
- [End-to-End Differentiable Proving](https://mlsanity.com/paper/1705.11040/) (2017)
- [Knowledge Graph Completion via Complex Tensor Factorization](https://mlsanity.com/paper/1702.06879/) (2017)
- [Plausible Reasoning about EL-Ontologies using Concept Interpolation](https://mlsanity.com/paper/2006.14437/) (2020)

## Built on by (most cited first, 2 of 2)

- [Learning Permutation-Invariant Embeddings for Description Logic Concepts](https://mlsanity.com/paper/2303.01844/) (2023)
- [From numerical proportions to analogical proportions between probabilities](https://mlsanity.com/paper/2606.23029/) (2026)

## Abstract (arXiv)

Ontologies formalise how the concepts from a given domain are interrelated. Despite their clear potential as a backbone for explainable AI, existing ontologies tend to be highly incomplete, which acts as a significant barrier to their more widespread adoption. To mitigate this issue, we present a mechanism to infer plausible missing knowledge, which relies on reasoning by analogy. To the best of our knowledge, this is the first paper that studies analogical reasoning within the setting of description logic ontologies. After showing that the standard formalisation of analogical proportion has important limitations in this setting, we introduce an alternative semantics based on bijective mappings between sets of features. We then analyse the properties of analogies under the proposed semantics, and show among others how it enables two plausible inference patterns: rule translation and rule extrapolation.