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

• URL: http://arxiv.org/abs/2605.25985v1
• Date: Mon, 25 May 2026 16:04:57 GMT
• Title: Neural Scalable Symbolic Search Framework for Complex Logical Queries with Multiple Free Variables
• Abstract summary: Complex Query Answering (CQA) is a fundamental knowledge representation and reasoning task over incomplete knowledge graphs (KGs)<n>It requires ranking answers in $mathcalEk$, where $mathcalEk$ denotes the entity set of a KG.<n>Existing benchmarks and methods rely on marginal rankings over individual variables; however, marginal rankings are a poor proxy for the true joint ranking of variables.<n>We propose Neural Scalable Symbolic Search (NS3), a framework that approximates joint ranking without enumerating $mathcalEk$.
• Score: 55.952069550106906
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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