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

2025-09-13

AI Summary

To address the challenge of balancing logical rigor and computational efficiency in answering existential first-order logic (EFO₁) queries over incomplete knowledge graphs, this paper proposes a neuro-symbolic integration framework. Our method introduces a grounding–Skolemization bipartite analytical architecture, incorporating a differentiable Skolemization module and a neural negation operator, jointly optimized under logical constraints to ensure theoretical completeness and logical consistency. We further unify efficient symbolic reasoning with representation learning via a vector-symbolic architecture, geometric–logical joint optimization, and neural-logical fusion techniques. Experiments demonstrate that our approach significantly outperforms existing Skolemization-based methods across multiple benchmarks, reduces inference cost by several orders of magnitude compared to traditional grounding, and maintains high accuracy and strong generalization capability.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Machine Learning: Neuro-Symbolic Learning

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Addresses trade-off between logical soundness and computational efficiency
• Proposes neuro-symbolic framework for complex query answering
• Ensures logical consistency while reducing combinatorial explosion

Innovation

• Differentiable Skolemization module for query answering
• Neural negator with logical constraint optimization
• Vector Symbolic Architecture unifying geometric and logical requirements