From Grounding to Skolemization: A Logic-Constrained Vector Symbolic Architecture for Complex Query Answering

• URL: http://arxiv.org/abs/2509.10837v1
• Date: Sat, 13 Sep 2025 14:59:00 GMT
• Title: From Grounding to Skolemization: A Logic-Constrained Vector Symbolic Architecture for Complex Query Answering
• Authors: Yuyin Lu, Hegang Chen, Yanghui Rao,
• Abstract summary: Complex Query Answering (CQA) over incomplete Knowledge Graphs (KGs) faces a fundamental trade-off between logical soundness and computational efficiency.<n>This work establishes the Grounding-Skolemization dichotomy for systematically analyzing CQA methods through the lens of formal logic.<n>We propose the Logic-constrained Symbolic Vector Architecture (LVSA), a neuro-symbolic framework that unifies a differentiable Skolemization module and a neural negator.
• Score: 14.380920038542287
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Complex Query Answering (CQA) over incomplete Knowledge Graphs (KGs), typically formalized as reasoning with Existential First-Order predicate logic with one free variable (EFO$_1$), faces a fundamental trade-off between logical soundness and computational efficiency. This work establishes the Grounding-Skolemization dichotomy for systematically analyzing CQA methods through the lens of formal logic. While Grounding-based methods inherently suffer from combinatorial explosion, most Skolemization-based methods neglect to explicitly model Skolem functions and compromise logical consistency. To address these limitations, we propose the Logic-constrained Vector Symbolic Architecture (LVSA), a neuro-symbolic framework that unifies a differentiable Skolemization module and a neural negator, as well as a logical constraint-driven optimization protocol to harmonize geometric and logical requirements. Theoretically, LVSA guarantees universality for all EFO$_1$ queries. Empirically, it outperforms state-of-the-art Skolemization-based methods and reduces inference costs by orders of magnitude compared to Grounding-based baselines.

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