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Rethinking Complex Queries on Knowledge Graphs with Neural Link Predictors

Hang Yin, Zihao Wang, Yangqiu Song

TL;DR

A new neural-symbolic method, Fuzzy Inference with Truth value (FIT), where the neural link predictors are equipped with fuzzy logic theory to support end-to-end learning using complex queries with provable reasoning capability is proposed.

Abstract

Reasoning on knowledge graphs is a challenging task because it utilizes observed information to predict the missing one. Particularly, answering complex queries based on first-order logic is one of the crucial tasks to verify learning to reason abilities for generalization and composition. Recently, the prevailing method is query embedding which learns the embedding of a set of entities and treats logic operations as set operations and has shown great empirical success. Though there has been much research following the same formulation, many of its claims lack a formal and systematic inspection. In this paper, we rethink this formulation and justify many of the previous claims by characterizing the scope of queries investigated previously and precisely identifying the gap between its formulation and its goal, as well as providing complexity analysis for the currently investigated queries. Moreover, we develop a new dataset containing ten new types of queries with features that have never been considered and therefore can provide a thorough investigation of complex queries. Finally, we propose a new neural-symbolic method, Fuzzy Inference with Truth value (FIT), where we equip the neural link predictors with fuzzy logic theory to support end-to-end learning using complex queries with provable reasoning capability. Empirical results show that our method outperforms previous methods significantly in the new dataset and also surpasses previous methods in the existing dataset at the same time.

Rethinking Complex Queries on Knowledge Graphs with Neural Link Predictors

TL;DR

A new neural-symbolic method, Fuzzy Inference with Truth value (FIT), where the neural link predictors are equipped with fuzzy logic theory to support end-to-end learning using complex queries with provable reasoning capability is proposed.

Abstract

Reasoning on knowledge graphs is a challenging task because it utilizes observed information to predict the missing one. Particularly, answering complex queries based on first-order logic is one of the crucial tasks to verify learning to reason abilities for generalization and composition. Recently, the prevailing method is query embedding which learns the embedding of a set of entities and treats logic operations as set operations and has shown great empirical success. Though there has been much research following the same formulation, many of its claims lack a formal and systematic inspection. In this paper, we rethink this formulation and justify many of the previous claims by characterizing the scope of queries investigated previously and precisely identifying the gap between its formulation and its goal, as well as providing complexity analysis for the currently investigated queries. Moreover, we develop a new dataset containing ten new types of queries with features that have never been considered and therefore can provide a thorough investigation of complex queries. Finally, we propose a new neural-symbolic method, Fuzzy Inference with Truth value (FIT), where we equip the neural link predictors with fuzzy logic theory to support end-to-end learning using complex queries with provable reasoning capability. Empirical results show that our method outperforms previous methods significantly in the new dataset and also surpasses previous methods in the existing dataset at the same time.
Paper Structure (45 sections, 16 theorems, 42 equations, 6 figures, 12 tables, 2 algorithms)

This paper contains 45 sections, 16 theorems, 42 equations, 6 figures, 12 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Knowledge graphs
  4. ${\textsc{EFO}_1}$ queries and answers
  5. The limitation of previous formulation
  6. The syntactical closure of previous formulation: Tree-form queries
  7. ${\textsc{TF}}$ queries deviate from the goal of ${\textsc{EFO}_1}$ queries
  8. Gaps between ${\textsc{TF}}$ and ${\textsc{EFO}_1}$ query
  9. A graph-theoretical description of ${\textsc{EFO}_1}$ queries
  10. Syntatical gap between ${\textsc{TF}}$ and ${\textsc{EFO}_1}$ queries
  11. Complexity gap between ${\textsc{TF}}$ and ${\textsc{EFO}_1}$ queries
  12. Methodology
  13. Fuzzy truth value definition
  14. Differentiable neural matrix construction
  15. Forward inference with truth value
  16. ...and 30 more sections

Key Result

Proposition 9

In DNFMore generally, this conclusion is true in every prenex normal form, which is a pre-requisite for query embedding method wang_benchmarking_2021., the universal quantifier may exist in ${\textsc{TF}}$ queries, thus the family of ${\textsc{TF}}$ query is not a subset of ${\textsc{EFO}_1}$.

Figures (6)

  • Figure 1: Representation of the tree form query "pni". We note that this kind of representation requires explicit set operators in the graph, the corresponding lines are dotted.
  • Figure 2: A diagram for the differences between the Tree-Form queries (orange blocks) and the ${\textsc{EFO}_1}$ queries (black box). ${\textsc{EFO}_1}$ queries are categorized by their query graphs. Some Tree-Form queries are not of ${\textsc{EFO}_1}$.
  • Figure 3: A given query "Find someone who has such two papers: s/he is the corresponding author of the first paper which has been awarded Outstanding Paper, s/he is the author but not the first author of the second paper which has been published and been cited by the first paper." can be represented as such query graphs. The formal existential formula is also given at the top.
  • Figure 4: A toy example to show the process of FIT, the vector indicates the fuzzy set of the corresponding node has been updated in this step. The query graph follows Figure \ref{['fig:query graph']} with the grounded entity and relation omitted.
  • Figure 5: Query graphs of each real ${\textsc{EFO}_1}$ formula. Naming convention: l "existential leaf", m "multi graph", c for "circle". We also follow the previous convention: "i" for intersection, "p" for projection, and "n" for negation. The representation of query graphs follows Figure \ref{['fig:query graph']}.
  • ...and 1 more figures

Theorems & Definitions (42)

  • Definition 1: Terms
  • Definition 2: Atomic Formula
  • Definition 3: Existential First Order Formula
  • Remark 4: Query and sentence
  • Definition 5: Substitution
  • Definition 6: The Answer Set of ${\textsc{EFO}_1}$ Query
  • Definition 7: Disjunctive Normal Form
  • Definition 8: Tree-Form Query
  • Proposition 9
  • Example 10
  • ...and 32 more