Neural Scalable Symbolic Search Framework for Complex Logical Queries with Multiple Free Variables

2026-05-25

AI Summary

This work addresses the challenging problem of joint answer ranking for multi-free-variable logical queries (EFOₖ with k > 1) over incomplete knowledge graphs, where the solution space grows exponentially with the number of variables, rendering exhaustive enumeration intractable. To tackle this, the authors propose NS3, a novel framework that combines neural-symbolic search with dynamic budget control to progressively reduce query dimensionality. NS3 first computes candidate answers via marginalized subqueries and then fuses free variables into hyper-nodes, dynamically pruning their domains to avoid full enumeration. This approach enables, for the first time, efficient approximate joint ranking for EFOₖ queries, overcoming the limitations of existing methods that rely solely on marginal ranking. The authors also introduce the first benchmark supporting joint ranking evaluation for k = 3. Experiments on three standard datasets demonstrate that NS3 significantly improves joint ranking performance while maintaining strong marginal ranking accuracy. Code and the new benchmark are publicly released.

Abstract

Complex Query Answering (CQA) is a fundamental knowledge representation and reasoning task over incomplete knowledge graphs (KGs). Answering existential first-order queries with $k$ free variables (i.e., $\text{EFO}_k$ queries) is a crucial yet challenging problem, as it requires ranking answer tuples in $\mathcal{E}^k$, where $\mathcal{E}$ denotes the entity set of a KG. This quickly becomes intractable as $k$ grows. Consequently, existing benchmarks and methods rely on marginal rankings over individual variables; however, marginal rankings are a poor proxy for the true joint ranking of tuples. Building on neural symbolic search for $\text{EFO}_1$ queries, we propose Neural Scalable Symbolic Search (NS3), a budgeted framework that approximates joint ranking without enumerating $\mathcal{E}^k$. NS3 (i) answers marginalized sub-queries to obtain necessary candidate sets, (ii) merges multiple free variables into hypernodes whose domains are pruned and controlled by a dynamic budget $B$, and (iii) progressively reduces an $\text{EFO}_k$ query to an $\text{EFO}_{k-1}$ query over a budgeted reduced domain. Across three standard KG datasets, NS3 substantially improves joint ranking performance while retaining strong marginal accuracy. We further release a joint-ranking benchmark that extends existing $\text{EFO}_1$ datasets to $k=3$, enabling systematic evaluation of multi-variable queries. Our code is provided in https://github.com/HKUST-KnowComp/NS3_KDD2026.

Problem

• Complex Query Answering
• Existential First-Order Queries
• Joint Ranking
• Knowledge Graphs
• Multiple Free Variables

Innovation

• Neural Symbolic Search
• Complex Query Answering
• Joint Ranking
• Budgeted Search
• Knowledge Graph Reasoning