# DAGE: DAG Query Answering via Relational Combinator with Logical Constraints

arXiv: https://arxiv.org/abs/2410.22105 · HTML: https://mlsanity.com/paper/2410.22105/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 26 references that are in the map.
- First posted on arXiv 29 Oct 2024.

## Builds on (most cited first, 14 of 14)

- [DeepPath: A Reinforcement Learning Method for Knowledge Graph Reasoning](https://mlsanity.com/paper/1707.06690/) (2017)
- [Query2box: Reasoning over Knowledge Graphs in Vector Space using Box Embeddings](https://mlsanity.com/paper/2002.05969/) (2020)
- [Embedding Logical Queries on Knowledge Graphs](https://mlsanity.com/paper/1806.01445/) (2018)
- [Multi-Hop Knowledge Graph Reasoning with Reward Shaping](https://mlsanity.com/paper/1808.10568/) (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)
- [Answering Complex Queries in Knowledge Graphs with Bidirectional Sequence Encoders](https://mlsanity.com/paper/2004.02596/) (2020)
- [Faithiful Embeddings for EL++ Knowledge Bases](https://mlsanity.com/paper/2201.09919/) (2022)
- [Dual Box Embeddings for the Description Logic EL++](https://mlsanity.com/paper/2301.11118/) (2023)
- [Description Logic EL++ Embeddings with Intersectional Closure](https://mlsanity.com/paper/2202.14018/) (2022)
- [Ontology Embedding: A Survey of Methods, Applications and Resources](https://mlsanity.com/paper/2406.10964/) (2024)
- [Is Complex Query Answering Really Complex?](https://mlsanity.com/paper/2410.12537/) (2024)
- [Approximating Probabilistic Inference in Statistical EL with Knowledge Graph Embeddings](https://mlsanity.com/paper/2407.11821/) (2024)

## Built on by (most cited first, 4 of 4)

- [SEMMA: A Semantic Aware Knowledge Graph Foundation Model](https://mlsanity.com/paper/2505.20422/) (2025)
- [Predicate-Conditional Conformalized Answer Sets for Knowledge Graph Embeddings](https://mlsanity.com/paper/2505.16877/) (2025)
- [Neural Scalable Symbolic Search Framework for Complex Logical Queries with Multiple Free Variables](https://mlsanity.com/paper/2605.25985/) (2026)
- [SCAIR: Schema-Conditioned Agentic Iterative Reasoning for Enterprise Knowledge Graphs](https://mlsanity.com/paper/2607.22571/) (2026)

## Abstract (arXiv)

Predicting answers to queries over knowledge graphs is called a complex reasoning task because answering a query requires subdividing it into subqueries. Existing query embedding methods use this decomposition to compute the embedding of a query as the combination of the embedding of the subqueries. This requirement limits the answerable queries to queries having a single free variable and being decomposable, which are called tree-form queries and correspond to the SROI^- description logic. In this paper, we define a more general set of queries, called DAG queries and formulated in the ALCOIR description logic, propose a query embedding method for them, called DAGE, and a new benchmark to evaluate query embeddings on them. Given the computational graph of a DAG query, DAGE combines the possibly multiple paths between two nodes into a single path with a trainable operator that represents the intersection of relations and learns DAG-DL from tautologies. We show that it is possible to implement DAGE on top of existing query embedding methods, and we empirically measure the improvement of our method over the results of vanilla methods evaluated in tree-form queries that approximate the DAG queries of our proposed benchmark.