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DAGE: DAG Query Answering via Relational Combinator with Logical Constraints

Yunjie He, Bo Xiong, Daniel Hernández, Yuqicheng Zhu, Evgeny Kharlamov, Steffen Staab

TL;DR

This work broadens complex query answering in knowledge graphs from tree-form to DAG queries by introducing DAGs in the $\mathcal{ALCOIR}$ framework. It presents DAGE, a plug-in relational combinator that merges multiple relation paths via a learnable $\operatorname{RCombiner}$, enabling existing QE methods to handle DAG queries. The authors attach soft tautology regularizers (monotonicity and restricted conjunction preserving) and introduce six DAG query types across three benchmarks (NELL-DAG, FB15k-237-DAG, FB15k-DAG) to rigorously evaluate performance. Empirically, DAGE yields substantial improvements on DAG queries while preserving tree-form performance, highlighting its practical impact for more expressive reasoning in knowledge graphs, albeit with limitations in hard constraint enforcement and true complex-boolean queries to explore in future work.

Abstract

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 $\mathcal{SROI}^-$ description logic. In this paper, we define a more general set of queries, called DAG queries and formulated in the $\mathcal{ALCOIR}$ 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.

DAGE: DAG Query Answering via Relational Combinator with Logical Constraints

TL;DR

This work broadens complex query answering in knowledge graphs from tree-form to DAG queries by introducing DAGs in the framework. It presents DAGE, a plug-in relational combinator that merges multiple relation paths via a learnable , enabling existing QE methods to handle DAG queries. The authors attach soft tautology regularizers (monotonicity and restricted conjunction preserving) and introduce six DAG query types across three benchmarks (NELL-DAG, FB15k-237-DAG, FB15k-DAG) to rigorously evaluate performance. Empirically, DAGE yields substantial improvements on DAG queries while preserving tree-form performance, highlighting its practical impact for more expressive reasoning in knowledge graphs, albeit with limitations in hard constraint enforcement and true complex-boolean queries to explore in future work.

Abstract

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 description logic. In this paper, we define a more general set of queries, called DAG queries and formulated in the 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.

Paper Structure

This paper contains 39 sections, 3 theorems, 32 equations, 6 figures, 13 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Tree-Form and the DAG Queries
  4. Syntax of Queries
  5. Computation Graphs
  6. Relaxing Non Tree-Form DAG queries
  7. DAG Query Answering with Relational Combinator
  8. Base Query Embedding Methods Interface
  9. Role Embeddings
  10. Concept Embeddings
  11. Insideness
  12. The Relational Combinator
  13. Encouraging Tautologies
  14. Monotonicity
  15. Restricted conjunction preserving
  16. ...and 24 more sections

Key Result

proposition 1

Given two role descriptions $R$ and $S$, and an individual name $a$, the following equivalences hold:

Figures (6)

  • Figure 1: Query structures considered in the experiments, where anchor entities and relations are to be specified to instantiate logical queries. Each structure is named using abbreviations: "s" for split, "p" for projection, "i" for intersection, "u" for union, and "n" for negation. For instance, "2s" indicates a structure with two splitting edges.
  • Figure 2: Overlap proportion between DAG and Tree-Form query answers from the NELL-DAG Easy test dataset.
  • Figure 3: Average percentage of improvement from baseline model to baseline (DAGE) for different overlap ratios
  • Figure 4: Transformation from DAG query to relaxed tree-form query
  • Figure 5: Proportion of overlap between DAG query answers and the corresponding Tree-Form query answers from FB15k-DAG-QA Easy test dataset.
  • ...and 1 more figures

Theorems & Definitions (15)

  • definition 1: Syntax of $\mathcal{ALCOIR}$ Concept and Role Descriptions
  • definition 2: Syntax of $\mathcal{ALCOIR}$ Knowledge Bases
  • definition 3: Interpretations
  • definition 4: Semantics of $\mathcal{ALCOIR}$ Knowledge Bases
  • definition 5: Entailment
  • definition 6: Knowledge Graph AConE
  • definition 7: Knowledge Graphs Query Answers
  • definition 8: Tree-Form and DAG queries
  • proposition 1
  • definition 9: Computation Graph
  • ...and 5 more