# TAR: Neural Logical Reasoning across TBox and ABox

arXiv: https://arxiv.org/abs/2205.14591 · HTML: https://mlsanity.com/paper/2205.14591/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 17 of its 47 references that are in the map.
- First posted on arXiv 29 May 2022.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Query2box: Reasoning over Knowledge Graphs in Vector Space using Box Embeddings](https://mlsanity.com/paper/2002.05969/) (2020)
- [Beta Embeddings for Multi-Hop Logical Reasoning in Knowledge Graphs](https://mlsanity.com/paper/2010.11465/) (2020)
- [Improving Conversational Recommender Systems via Knowledge Graph based Semantic Fusion](https://mlsanity.com/paper/2007.04032/) (2020)
- [Embedding Logical Queries on Knowledge Graphs](https://mlsanity.com/paper/1806.01445/) (2018)
- [Complex Query Answering with Neural Link Predictors](https://mlsanity.com/paper/2011.03459/) (2020)
- [ConE: Cone Embeddings for Multi-Hop Reasoning over Knowledge Graphs](https://mlsanity.com/paper/2110.13715/) (2021)
- [Neural-Symbolic Models for Logical Queries on Knowledge Graphs](https://mlsanity.com/paper/2205.10128/) (2022)
- [EL Embeddings: Geometric construction of models for the Description Logic EL ++](https://mlsanity.com/paper/1902.10499/) (2019)
- [Universal Representation Learning of Knowledge Bases by Jointly Embedding Instances and Ontological Concepts](https://mlsanity.com/paper/2103.08115/) (2021)
- [Self-Supervised Hyperboloid Representations from Logical Queries over Knowledge Graphs](https://mlsanity.com/paper/2012.13023/) (2020)
- [OPA2Vec: combining formal and informal content of biomedical ontologies to improve similarity-based prediction](https://mlsanity.com/paper/1804.10922/) (2018)
- [Logic Embeddings for Complex Query Answering](https://mlsanity.com/paper/2103.00418/) (2021)
- [Analyzing Differentiable Fuzzy Implications](https://mlsanity.com/paper/2006.03472/) (2020)
- [Positive-Unlabeled Learning with Adversarial Data Augmentation for Knowledge Graph Completion](https://mlsanity.com/paper/2205.00904/) (2022)
- [Fuzzy Logic Based Logical Query Answering on Knowledge Graphs](https://mlsanity.com/paper/2108.02390/) (2021)
- [Bio-JOIE: Joint Representation Learning of Biological Knowledge Bases](https://mlsanity.com/paper/2103.04283/) (2021)

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

- [Neural Graph Reasoning: Complex Logical Query Answering Meets Graph Databases](https://mlsanity.com/paper/2303.14617/) (2023)
- [ULLER: A Unified Language for Learning and Reasoning](https://mlsanity.com/paper/2405.00532/) (2024)

## Abstract (arXiv)

Many ontologies, i.e., Description Logic (DL) knowledge bases, have been developed to provide rich knowledge about various domains. An ontology consists of an ABox, i.e., assertion axioms between two entities or between a concept and an entity, and a TBox, i.e., terminology axioms between two concepts. Neural logical reasoning (NLR) is a fundamental task to explore such knowledge bases, which aims at answering multi-hop queries with logical operations based on distributed representations of queries and answers. While previous NLR methods can give specific entity-level answers, i.e., ABox answers, they are not able to provide descriptive concept-level answers, i.e., TBox answers, where each concept is a description of a set of entities. In other words, previous NLR methods only reason over the ABox of an ontology while ignoring the TBox. In particular, providing TBox answers enables inferring the explanations of each query with descriptive concepts, which make answers comprehensible to users and are of great usefulness in the field of applied ontology. In this work, we formulate the problem of neural logical reasoning across TBox and ABox (TA-NLR), solving which needs to address challenges in incorporating, representing, and operating on concepts. We propose an original solution named TAR for TA-NLR. Firstly, we incorporate description logic based ontological axioms to provide the source of concepts. Then, we represent concepts and queries as fuzzy sets, i.e., sets whose elements have degrees of membership, to bridge concepts and queries with entities. Moreover, we design operators involving concepts on top of fuzzy set representation of concepts and queries for optimization and inference. Extensive experimental results on two real-world datasets demonstrate the effectiveness of TAR for TA-NLR.