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

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.

Efficient and Scalable Neural Symbolic Search for Knowledge Graph Complex Query Answering

Complex Query Answering (CQA) aims to retrieve answer sets for complex logical formulas from incomplete knowledge graphs, which is a crucial yet challenging task in knowledge graph reasoning. While neuro-symbolic search utilized neural link predictions achieve superior accuracy, they encounter significant complexity bottlenecks: (i) Data complexity typically scales quadratically with the number of entities in the knowledge graph, and (ii) Query complexity becomes NP-hard for cyclic queries. Consequently, these approaches struggle to effectively scale to larger knowledge graphs and more complex queries. To address these challenges, we propose an efficient and scalable symbolic search framework. First, we propose two constraint strategies to compute neural logical indices to reduce the domain of variables, thereby decreasing the data complexity of symbolic search. Additionally, we introduce an approximate algorithm based on local search to tackle the NP query complexity of cyclic queries. Experiments on various CQA benchmarks demonstrate that our framework reduces the computational load of symbolic methods by 90\% while maintaining nearly the same performance, thus alleviating both efficiency and scalability issues.